[{"external_id":{"arxiv":["2211.14046"]},"oa":"1","citation":{"mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.” <i>Annales Henri Poincaré</i>, vol. 25, no. 6, Springer Science and Business Media LLC, 2023, pp. 2877–940, doi:<a href=\"https://doi.org/10.1007/s00023-023-01369-z\">10.1007/s00023-023-01369-z</a>.","bibtex":"@article{Hinrichs_Matte_2023, title={Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions}, volume={25}, DOI={<a href=\"https://doi.org/10.1007/s00023-023-01369-z\">10.1007/s00023-023-01369-z</a>}, number={6}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2023}, pages={2877–2940} }","ama":"Hinrichs B, Matte O. Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions. <i>Annales Henri Poincaré</i>. 2023;25(6):2877-2940. doi:<a href=\"https://doi.org/10.1007/s00023-023-01369-z\">10.1007/s00023-023-01369-z</a>","ieee":"B. Hinrichs and O. Matte, “Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions,” <i>Annales Henri Poincaré</i>, vol. 25, no. 6, pp. 2877–2940, 2023, doi: <a href=\"https://doi.org/10.1007/s00023-023-01369-z\">10.1007/s00023-023-01369-z</a>.","apa":"Hinrichs, B., &#38; Matte, O. (2023). Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions. <i>Annales Henri Poincaré</i>, <i>25</i>(6), 2877–2940. <a href=\"https://doi.org/10.1007/s00023-023-01369-z\">https://doi.org/10.1007/s00023-023-01369-z</a>","short":"B. Hinrichs, O. Matte, Annales Henri Poincaré 25 (2023) 2877–2940.","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.” <i>Annales Henri Poincaré</i> 25, no. 6 (2023): 2877–2940. <a href=\"https://doi.org/10.1007/s00023-023-01369-z\">https://doi.org/10.1007/s00023-023-01369-z</a>."},"publisher":"Springer Science and Business Media LLC","_id":"63635","page":"2877-2940","volume":25,"user_id":"99427","status":"public","date_created":"2026-01-16T08:39:40Z","department":[{"_id":"799"}],"type":"journal_article","issue":"6","publication":"Annales Henri Poincaré","extern":"1","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1"}],"doi":"10.1007/s00023-023-01369-z","author":[{"id":"99427","full_name":"Hinrichs, Benjamin","first_name":"Benjamin","orcid":"0000-0001-9074-1205","last_name":"Hinrichs"},{"full_name":"Matte, Oliver","first_name":"Oliver","last_name":"Matte"}],"publication_identifier":{"issn":["1424-0637","1424-0661"]},"year":"2023","title":"Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions","article_type":"original","intvolume":"        25","publication_status":"published","date_updated":"2026-01-16T09:05:26Z"},{"external_id":{"arxiv":["2205.09189"]},"oa":"1","citation":{"mla":"Hinrichs, Benjamin, et al. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 528, no. 1, 127558, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>.","ama":"Hinrichs B, Janssen DW, Ziebell J. Super-Gaussian decay of exponentials: A sufficient condition. <i>Journal of Mathematical Analysis and Applications</i>. 2023;528(1). doi:<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>","bibtex":"@article{Hinrichs_Janssen_Ziebell_2023, title={Super-Gaussian decay of exponentials: A sufficient condition}, volume={528}, DOI={<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>}, number={1127558}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}, year={2023} }","apa":"Hinrichs, B., Janssen, D. W., &#38; Ziebell, J. (2023). Super-Gaussian decay of exponentials: A sufficient condition. <i>Journal of Mathematical Analysis and Applications</i>, <i>528</i>(1), Article 127558. <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">https://doi.org/10.1016/j.jmaa.2023.127558</a>","ieee":"B. Hinrichs, D. W. Janssen, and J. Ziebell, “Super-Gaussian decay of exponentials: A sufficient condition,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 528, no. 1, Art. no. 127558, 2023, doi: <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>.","chicago":"Hinrichs, Benjamin, Daan W. Janssen, and Jobst Ziebell. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” <i>Journal of Mathematical Analysis and Applications</i> 528, no. 1 (2023). <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">https://doi.org/10.1016/j.jmaa.2023.127558</a>.","short":"B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and Applications 528 (2023)."},"publisher":"Elsevier BV","_id":"46100","user_id":"99427","volume":528,"status":"public","date_created":"2023-07-20T05:08:49Z","type":"journal_article","keyword":["Applied Mathematics","Analysis"],"department":[{"_id":"799"}],"issue":"1","publication":"Journal of Mathematical Analysis and Applications","main_file_link":[{"open_access":"1"}],"article_number":"127558","language":[{"iso":"eng"}],"doi":"10.1016/j.jmaa.2023.127558","year":"2023","title":"Super-Gaussian decay of exponentials: A sufficient condition","author":[{"id":"99427","orcid":"0000-0001-9074-1205","first_name":"Benjamin","last_name":"Hinrichs","full_name":"Hinrichs, Benjamin"},{"last_name":"Janssen","first_name":"Daan W.","full_name":"Janssen, Daan W."},{"full_name":"Ziebell, Jobst","last_name":"Ziebell","first_name":"Jobst"}],"publication_identifier":{"issn":["0022-247X"]},"date_updated":"2026-01-16T09:04:39Z","publication_status":"published","intvolume":"       528"},{"external_id":{"arxiv":["2103.05667"]},"citation":{"bibtex":"@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical correspondence}, volume={16}, DOI={<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>}, number={10}, journal={Analysis &#38; PDE}, publisher={MSP}, author={Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }","ama":"Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence. <i>Analysis &#38; PDE</i>. 2023;16(10):2241–2265. doi:<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>","mla":"Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” <i>Analysis &#38; PDE</i>, vol. 16, no. 10, MSP, 2023, pp. 2241–2265, doi:<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>.","chicago":"Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical Correspondence.” <i>Analysis &#38; PDE</i> 16, no. 10 (2023): 2241–2265. <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>.","short":"J. Hilgert, T. Weich, L.L. Wolf, Analysis &#38; PDE 16 (2023) 2241–2265.","ieee":"J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,” <i>Analysis &#38; PDE</i>, vol. 16, no. 10, pp. 2241–2265, 2023, doi: <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>.","apa":"Hilgert, J., Weich, T., &#38; Wolf, L. L. (2023). Higher rank quantum-classical correspondence. <i>Analysis &#38; PDE</i>, <i>16</i>(10), 2241–2265. <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>"},"volume":16,"user_id":"49178","_id":"31190","publisher":"MSP","page":"2241–2265","status":"public","department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"type":"journal_article","date_created":"2022-05-11T10:41:35Z","abstract":[{"text":"For a compact Riemannian locally symmetric space $\\Gamma\\backslash G/K$ of\r\narbitrary rank we determine the location of certain Ruelle-Taylor resonances\r\nfor the Weyl chamber action. We provide a Weyl-lower bound on an appropriate\r\ncounting function for the Ruelle-Taylor resonances and establish a spectral gap\r\nwhich is uniform in $\\Gamma$ if $G/K$ is irreducible of higher rank. This is\r\nachieved by proving a quantum-classical correspondence, i.e. a\r\n1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant\r\nstates and joint eigenfunctions of the algebra of invariant differential\r\noperators on $G/K$.","lang":"eng"}],"issue":"10","publication":"Analysis & PDE","doi":"https://doi.org/10.2140/apde.2023.16.2241","language":[{"iso":"eng"}],"intvolume":"        16","date_updated":"2026-02-18T10:39:36Z","author":[{"last_name":"Hilgert","first_name":"Joachim","full_name":"Hilgert, Joachim","id":"220"},{"id":"49178","full_name":"Weich, Tobias","first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919"},{"id":"45027","first_name":"Lasse Lennart","last_name":"Wolf","orcid":"0000-0001-8893-2045","full_name":"Wolf, Lasse Lennart"}],"year":"2023","title":"Higher rank quantum-classical correspondence"},{"date_updated":"2026-02-18T10:41:07Z","intvolume":"       398","title":"Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems","year":"2023","status":"public","author":[{"first_name":"Philipp","last_name":"Schütte","full_name":"Schütte, Philipp","id":"50168"},{"id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias","full_name":"Weich, Tobias"},{"full_name":"Barkhofen, Sonja","first_name":"Sonja","last_name":"Barkhofen","id":"48188"}],"doi":"https://doi.org/10.1007/s00220-022-04538-z","user_id":"49178","volume":398,"page":"655-678","language":[{"iso":"eng"}],"_id":"31059","abstract":[{"text":"In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.","lang":"eng"}],"publication":"Communications in Mathematical Physics","citation":{"ama":"Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. <i>Communications in Mathematical Physics</i>. 2023;398:655-678. doi:<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>","bibtex":"@article{Schütte_Weich_Barkhofen_2023, title={Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}, volume={398}, DOI={<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>}, journal={Communications in Mathematical Physics}, author={Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}, year={2023}, pages={655–678} }","mla":"Schütte, Philipp, et al. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” <i>Communications in Mathematical Physics</i>, vol. 398, 2023, pp. 655–78, doi:<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>.","short":"P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics 398 (2023) 655–678.","chicago":"Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” <i>Communications in Mathematical Physics</i> 398 (2023): 655–78. <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>.","apa":"Schütte, P., Weich, T., &#38; Barkhofen, S. (2023). Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. <i>Communications in Mathematical Physics</i>, <i>398</i>, 655–678. <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>","ieee":"P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems,” <i>Communications in Mathematical Physics</i>, vol. 398, pp. 655–678, 2023, doi: <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>."},"type":"journal_article","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"},{"_id":"15"}],"external_id":{"arxiv":["2112.05791"]},"date_created":"2022-05-04T12:27:46Z"},{"user_id":"37888","ddc":["510"],"_id":"58097","language":[{"iso":"ger"}],"publisher":"WTM-Verlag","date_updated":"2025-01-08T08:17:40Z","has_accepted_license":"1","title":"Einblicke in ein Referenzmodell zur Analyse der Einführung von Vektoren in Schulbüchern","status":"public","year":"2023","corporate_editor":["IDMI-Primar Goethe-Universität Frankfurt"],"author":[{"full_name":"Mai, Tobias","first_name":"Tobias","last_name":"Mai"},{"id":"16274","full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"}],"type":"book_chapter","department":[{"_id":"363"}],"file":[{"creator":"krueter","date_created":"2025-01-08T08:17:16Z","file_name":"Mai aus Beitraege_2022___ISBN9783959872089-3.pdf","file_size":546218,"access_level":"closed","relation":"main_file","date_updated":"2025-01-08T08:17:16Z","file_id":"58098","success":1,"content_type":"application/pdf"}],"date_created":"2025-01-08T08:17:35Z","place":"Münster","file_date_updated":"2025-01-08T08:17:16Z","publication":"Beiträge zum Mathematikunterricht 2022. 56. 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Jahrestagung der Gesellschaft für Didaktik der Mathematik","citation":{"mla":"Lankeit, Elisa, and Rolf Biehler. “Das totale Differential und die Richtungsableitung – Eine Analyse mit Blick in ausgewählte Lehrbücher.” <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, edited by IDMI-Primar Goethe-Universität Frankfurt, WTM-Verlag, 2023.","bibtex":"@inbook{Lankeit_Biehler_2023, place={Münster}, title={Das totale Differential und die Richtungsableitung – Eine Analyse mit Blick in ausgewählte Lehrbücher}, booktitle={Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, publisher={WTM-Verlag}, author={Lankeit, Elisa and Biehler, Rolf}, editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2023} }","ama":"Lankeit E, Biehler R. Das totale Differential und die Richtungsableitung – Eine Analyse mit Blick in ausgewählte Lehrbücher. In: IDMI-Primar Goethe-Universität Frankfurt, ed. <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>. WTM-Verlag; 2023.","ieee":"E. Lankeit and R. Biehler, “Das totale Differential und die Richtungsableitung – Eine Analyse mit Blick in ausgewählte Lehrbücher,” in <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, IDMI-Primar Goethe-Universität Frankfurt, Ed. Münster: WTM-Verlag, 2023.","apa":"Lankeit, E., &#38; Biehler, R. (2023). Das totale Differential und die Richtungsableitung – Eine Analyse mit Blick in ausgewählte Lehrbücher. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>. WTM-Verlag.","chicago":"Lankeit, Elisa, and Rolf Biehler. “Das totale Differential und die Richtungsableitung – Eine Analyse mit Blick in ausgewählte Lehrbücher.” In <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, edited by IDMI-Primar Goethe-Universität Frankfurt. Münster: WTM-Verlag, 2023.","short":"E. Lankeit, R. Biehler, in: IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, WTM-Verlag, Münster, 2023."},"file":[{"date_created":"2025-01-08T08:19:33Z","creator":"krueter","file_id":"58100","content_type":"application/pdf","success":1,"relation":"main_file","date_updated":"2025-01-08T08:19:33Z","file_name":"Lankeit aus Beitraege_2022___ISBN9783959872089-2.pdf","access_level":"closed","file_size":536630}],"date_created":"2025-01-08T08:19:59Z","place":"Münster","type":"book_chapter","department":[{"_id":"363"}]},{"volume":10,"user_id":"220","language":[{"iso":"eng"}],"_id":"51383","page":"335-403","intvolume":"        10","publication_status":"published","date_updated":"2026-03-31T08:26:09Z","author":[{"full_name":"Hilgert, Joachim","first_name":"Joachim","last_name":"Hilgert","id":"220"},{"full_name":"Arends, C.","first_name":"C.","last_name":"Arends"}],"year":"2023","status":"public","title":"Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters","department":[{"_id":"91"}],"type":"journal_article","date_created":"2024-02-19T06:34:11Z","citation":{"mla":"Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One Locally Symmetric Spaces - The Case of Exceptional Parameters.” <i>J. de l’École Polytechnique — Mathématiques</i>, vol. 10, 2023, pp. 335–403.","apa":"Hilgert, J., &#38; Arends, C. (2023). Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters. <i>J. de l’École Polytechnique — Mathématiques</i>, <i>10</i>, 335–403.","ieee":"J. Hilgert and C. Arends, “Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters,” <i>J. de l’École polytechnique — Mathématiques</i>, vol. 10, pp. 335–403, 2023.","chicago":"Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One Locally Symmetric Spaces - The Case of Exceptional Parameters.” <i>J. de l’École Polytechnique — Mathématiques</i> 10 (2023): 335–403.","short":"J. Hilgert, C. Arends, J. de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","ama":"Hilgert J, Arends C. Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters. <i>J de l’École polytechnique — Mathématiques</i>. 2023;10:335-403.","bibtex":"@article{Hilgert_Arends_2023, title={Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters}, volume={10}, journal={J. de l’École polytechnique — Mathématiques}, author={Hilgert, Joachim and Arends, C.}, year={2023}, pages={335–403} }"},"publication":"J. de l'École polytechnique — Mathématiques"},{"language":[{"iso":"eng"}],"_id":"51384","page":"186-232","volume":343,"user_id":"220","author":[{"id":"220","last_name":"Hilgert","first_name":"Joachim","full_name":"Hilgert, Joachim"},{"full_name":"Glöckner, H.","last_name":"Glöckner","first_name":"H."}],"title":"Aspects of control theory on infinite-dimensional Lie groups and G-manifolds","year":"2023","status":"public","intvolume":"       343","date_updated":"2026-03-31T08:25:53Z","publication_status":"published","date_created":"2024-02-19T06:35:08Z","department":[{"_id":"91"}],"type":"journal_article","citation":{"bibtex":"@article{Hilgert_Glöckner_2023, title={Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}, volume={343}, journal={J. Diff. Equations}, author={Hilgert, Joachim and Glöckner, H.}, year={2023}, pages={186–232} }","ama":"Hilgert J, Glöckner H. Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. <i>J Diff Equations</i>. 2023;343:186-232.","mla":"Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” <i>J. Diff. Equations</i>, vol. 343, 2023, pp. 186–232.","chicago":"Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” <i>J. Diff. Equations</i> 343 (2023): 186–232.","short":"J. Hilgert, H. Glöckner, J. Diff. Equations 343 (2023) 186–232.","ieee":"J. Hilgert and H. Glöckner, “Aspects of control theory on infinite-dimensional Lie groups and G-manifolds,” <i>J. Diff. Equations</i>, vol. 343, pp. 186–232, 2023.","apa":"Hilgert, J., &#38; Glöckner, H. (2023). Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. <i>J. Diff. Equations</i>, <i>343</i>, 186–232."},"publication":"J. Diff. Equations"},{"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>This note is concerned with two families of operators related to the fractional Laplacian, the first arising from the Caffarelli-Silvestre extension problem and the second from the fractional heat equation. They both include the Poisson semigroup. We show that on a complete, connected, and non-compact Riemannian manifold of non-negative Ricci curvature, in both cases, the solution with <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n                  <mml:mi>L</mml:mi>\r\n                  <mml:mn>1</mml:mn>\r\n                </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula> initial data behaves asymptotically as the mass times the fundamental solution. Similar long-time convergence results remain valid on more general manifolds satisfying the Li-Yau two-sided estimate of the heat kernel. The situation changes drastically on hyperbolic space, and more generally on rank one non-compact symmetric spaces: we show that for the Poisson semigroup, the convergence to the Poisson kernel fails -but remains true under the additional assumption of radial initial data.</jats:p>","lang":"eng"}],"publication":"Potential Analysis","citation":{"short":"E. Papageorgiou, Potential Analysis (2023).","chicago":"Papageorgiou, Efthymia. “Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds.” <i>Potential Analysis</i>, 2023. <a href=\"https://doi.org/10.1007/s11118-023-10109-1\">https://doi.org/10.1007/s11118-023-10109-1</a>.","ieee":"E. Papageorgiou, “Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds,” <i>Potential Analysis</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s11118-023-10109-1\">10.1007/s11118-023-10109-1</a>.","apa":"Papageorgiou, E. (2023). Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds. <i>Potential Analysis</i>. <a href=\"https://doi.org/10.1007/s11118-023-10109-1\">https://doi.org/10.1007/s11118-023-10109-1</a>","bibtex":"@article{Papageorgiou_2023, title={Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds}, DOI={<a href=\"https://doi.org/10.1007/s11118-023-10109-1\">10.1007/s11118-023-10109-1</a>}, journal={Potential Analysis}, publisher={Springer Science and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2023} }","ama":"Papageorgiou E. Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds. <i>Potential Analysis</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s11118-023-10109-1\">10.1007/s11118-023-10109-1</a>","mla":"Papageorgiou, Efthymia. “Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds.” <i>Potential Analysis</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s11118-023-10109-1\">10.1007/s11118-023-10109-1</a>."},"type":"journal_article","keyword":["Analysis"],"department":[{"_id":"555"}],"date_created":"2024-04-17T13:17:37Z","publication_status":"published","date_updated":"2026-07-03T12:37:31Z","year":"2023","status":"public","title":"Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds","author":[{"id":"100325","last_name":"Papageorgiou","first_name":"Efthymia","full_name":"Papageorgiou, Efthymia"}],"publication_identifier":{"issn":["0926-2601","1572-929X"]},"user_id":"100325","doi":"10.1007/s11118-023-10109-1","language":[{"iso":"eng"}],"_id":"53540","publisher":"Springer Science and Business Media LLC"},{"type":"journal_article","keyword":["Applied Mathematics","Numerical Analysis","Analysis"],"department":[{"_id":"555"}],"date_created":"2024-04-17T13:16:39Z","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>The infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length <jats:italic>T</jats:italic> around a fixed origin when <jats:inline-formula><jats:alternatives><jats:tex-math>$$T \\rightarrow +\\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>T</mml:mi>\r\n                  <mml:mo>→</mml:mo>\r\n                  <mml:mo>+</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>. The aim of this note is to study its long-time asymptotics on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> of noncompact type and of general rank. This amounts to the behavior of solutions to the heat equation subject to the Doob transform induced by the ground spherical function. Unlike the standard Brownian motion, we observe in this case phenomena which are similar to the Euclidean setting, namely <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n                  <mml:mi>L</mml:mi>\r\n                  <mml:mn>1</mml:mn>\r\n                </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula> asymptotic convergence without requiring bi-<jats:italic>K</jats:italic>-invariance for initial data, and strong <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\infty }$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n                  <mml:mi>L</mml:mi>\r\n                  <mml:mi>∞</mml:mi>\r\n                </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula> convergence.</jats:p>"}],"publication":"Journal of Elliptic and Parabolic Equations","citation":{"mla":"Papageorgiou, Efthymia. “Asymptotics for the Infinite Brownian Loop on Noncompact Symmetric Spaces.” <i>Journal of Elliptic and Parabolic Equations</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s41808-023-00250-8\">10.1007/s41808-023-00250-8</a>.","bibtex":"@article{Papageorgiou_2023, title={Asymptotics for the infinite Brownian loop on noncompact symmetric spaces}, DOI={<a href=\"https://doi.org/10.1007/s41808-023-00250-8\">10.1007/s41808-023-00250-8</a>}, journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer Science and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2023} }","ama":"Papageorgiou E. Asymptotics for the infinite Brownian loop on noncompact symmetric spaces. <i>Journal of Elliptic and Parabolic Equations</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s41808-023-00250-8\">10.1007/s41808-023-00250-8</a>","ieee":"E. Papageorgiou, “Asymptotics for the infinite Brownian loop on noncompact symmetric spaces,” <i>Journal of Elliptic and Parabolic Equations</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s41808-023-00250-8\">10.1007/s41808-023-00250-8</a>.","apa":"Papageorgiou, E. (2023). Asymptotics for the infinite Brownian loop on noncompact symmetric spaces. <i>Journal of Elliptic and Parabolic Equations</i>. <a href=\"https://doi.org/10.1007/s41808-023-00250-8\">https://doi.org/10.1007/s41808-023-00250-8</a>","short":"E. Papageorgiou, Journal of Elliptic and Parabolic Equations (2023).","chicago":"Papageorgiou, Efthymia. “Asymptotics for the Infinite Brownian Loop on Noncompact Symmetric Spaces.” <i>Journal of Elliptic and Parabolic Equations</i>, 2023. <a href=\"https://doi.org/10.1007/s41808-023-00250-8\">https://doi.org/10.1007/s41808-023-00250-8</a>."},"doi":"10.1007/s41808-023-00250-8","user_id":"100325","_id":"53539","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"date_updated":"2026-07-03T12:36:17Z","publication_status":"published","status":"public","title":"Asymptotics for the infinite Brownian loop on noncompact symmetric spaces","year":"2023","publication_identifier":{"issn":["2296-9020","2296-9039"]},"author":[{"last_name":"Papageorgiou","first_name":"Efthymia","full_name":"Papageorgiou, Efthymia","id":"100325"}]},{"doi":"10.1007/978-3-030-79393-7_3","main_file_link":[{"url":"https://arxiv.org/pdf/1906.09075.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"date_updated":"2022-03-14T13:04:51Z","year":"2022","title":"ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation","publication_identifier":{"isbn":["978-3-030-79392-0"]},"author":[{"full_name":"Banholzer, Stefan","last_name":"Banholzer","first_name":"Stefan"},{"id":"32643","first_name":"Bennet","last_name":"Gebken","full_name":"Gebken, Bennet"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"},{"full_name":"Volkwein, Stefan","first_name":"Stefan","last_name":"Volkwein"}],"type":"book_chapter","department":[{"_id":"101"},{"_id":"655"}],"date_created":"2020-03-13T12:45:31Z","abstract":[{"text":"Multiobjective optimization plays an increasingly important role in modern\r\napplications, where several objectives are often of equal importance. The task\r\nin multiobjective optimization and multiobjective optimal control is therefore\r\nto compute the set of optimal compromises (the Pareto set) between the\r\nconflicting objectives. Since the Pareto set generally consists of an infinite\r\nnumber of solutions, the computational effort can quickly become challenging\r\nwhich is particularly problematic when the objectives are costly to evaluate as\r\nis the case for models governed by partial differential equations (PDEs). To\r\ndecrease the numerical effort to an affordable amount, surrogate models can be\r\nused to replace the expensive PDE evaluations. Existing multiobjective\r\noptimization methods using model reduction are limited either to low parameter\r\ndimensions or to few (ideally two) objectives. In this article, we present a\r\ncombination of the reduced basis model reduction method with a continuation\r\napproach using inexact gradients. The resulting approach can handle an\r\narbitrary number of objectives while yielding a significant reduction in\r\ncomputing time.","lang":"eng"}],"publication":"Non-Smooth and Complementarity-Based Distributed Parameter Systems","user_id":"47427","editor":[{"last_name":"Michael","first_name":"Hintermüller","full_name":"Michael, Hintermüller"},{"full_name":"Roland, Herzog","last_name":"Roland","first_name":"Herzog"},{"first_name":"Kanzow","last_name":"Christian","full_name":"Christian, Kanzow"},{"first_name":"Ulbrich","last_name":"Michael","full_name":"Michael, Ulbrich"},{"full_name":"Stefan, Ulbrich","last_name":"Stefan","first_name":"Ulbrich"}],"page":"43-76","_id":"16296","publisher":"Springer","status":"public","oa":"1","place":"Cham","citation":{"short":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, S. Volkwein, in: H. Michael, H. Roland, K. Christian, U. Michael, U. Stefan (Eds.), Non-Smooth and Complementarity-Based Distributed Parameter Systems, Springer, Cham, 2022, pp. 43–76.","chicago":"Banholzer, Stefan, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” In <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i>, edited by Hintermüller Michael, Herzog Roland, Kanzow Christian, Ulbrich Michael, and Ulbrich Stefan, 43–76. Cham: Springer, 2022. <a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">https://doi.org/10.1007/978-3-030-79393-7_3</a>.","ieee":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, and S. Volkwein, “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation,” in <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i>, H. Michael, H. Roland, K. Christian, U. Michael, and U. Stefan, Eds. Cham: Springer, 2022, pp. 43–76.","apa":"Banholzer, S., Gebken, B., Dellnitz, M., Peitz, S., &#38; Volkwein, S. (2022). ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In H. Michael, H. Roland, K. Christian, U. Michael, &#38; U. Stefan (Eds.), <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i> (pp. 43–76). Springer. <a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">https://doi.org/10.1007/978-3-030-79393-7_3</a>","bibtex":"@inbook{Banholzer_Gebken_Dellnitz_Peitz_Volkwein_2022, place={Cham}, title={ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">10.1007/978-3-030-79393-7_3</a>}, booktitle={Non-Smooth and Complementarity-Based Distributed Parameter Systems}, publisher={Springer}, author={Banholzer, Stefan and Gebken, Bennet and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, editor={Michael, Hintermüller and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich}, year={2022}, pages={43–76} }","ama":"Banholzer S, Gebken B, Dellnitz M, Peitz S, Volkwein S. ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In: Michael H, Roland H, Christian K, Michael U, Stefan U, eds. <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i>. Springer; 2022:43-76. doi:<a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">10.1007/978-3-030-79393-7_3</a>","mla":"Banholzer, Stefan, et al. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” <i>Non-Smooth and Complementarity-Based Distributed Parameter Systems</i>, edited by Hintermüller Michael et al., Springer, 2022, pp. 43–76, doi:<a href=\"https://doi.org/10.1007/978-3-030-79393-7_3\">10.1007/978-3-030-79393-7_3</a>."}},{"department":[{"_id":"101"},{"_id":"655"}],"type":"book_chapter","date_created":"2022-03-14T07:32:41Z","abstract":[{"lang":"eng","text":"With the ever increasing capabilities of sensors and controllers, autonomous driving is quickly becoming a reality. This disruptive change in the automotive industry poses major challenges for manufacturers as well as suppliers as entirely new design and testing strategies have to be developed to remain competitive. Most importantly, the complexity of autonomously driving vehicles in a complex, uncertain, and safety-critical environment requires new testing procedures to cover the almost infinite range of potential scenarios."}],"publication":"German Success Stories in Industrial Mathematics","doi":"10.1007/978-3-030-81455-7_23","series_title":"Mathematics in Industry","language":[{"iso":"eng"}],"intvolume":"        35","date_updated":"2022-03-14T07:42:01Z","publication_status":"published","author":[{"id":"47427","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"full_name":"Bannenberg, Sebastian","first_name":"Sebastian","last_name":"Bannenberg"}],"publication_identifier":{"isbn":["9783030814540","9783030814557"],"issn":["1612-3956","2198-3283"]},"title":"Efficient Virtual Design and Testing of Autonomous Vehicles","year":"2022","place":"Cham","citation":{"apa":"Peitz, S., Dellnitz, M., &#38; Bannenberg, S. (2022). Efficient Virtual Design and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, &#38; V. Schulz (Eds.), <i>German Success Stories in Industrial Mathematics</i> (Vol. 35). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">https://doi.org/10.1007/978-3-030-81455-7_23</a>","ieee":"S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing of Autonomous Vehicles,” in <i>German Success Stories in Industrial Mathematics</i>, vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham: Springer International Publishing, 2022.","short":"S. Peitz, M. Dellnitz, S. Bannenberg, in: H.G. Bock, K.-H. Küfer, P. Maas, A. Milde, V. Schulz (Eds.), German Success Stories in Industrial Mathematics, Springer International Publishing, Cham, 2022.","chicago":"Peitz, Sebastian, Michael Dellnitz, and Sebastian Bannenberg. “Efficient Virtual Design and Testing of Autonomous Vehicles.” In <i>German Success Stories in Industrial Mathematics</i>, edited by H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Vol. 35. Mathematics in Industry. Cham: Springer International Publishing, 2022. <a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">https://doi.org/10.1007/978-3-030-81455-7_23</a>.","mla":"Peitz, Sebastian, et al. “Efficient Virtual Design and Testing of Autonomous Vehicles.” <i>German Success Stories in Industrial Mathematics</i>, edited by H. G. Bock et al., vol. 35, Springer International Publishing, 2022, doi:<a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">10.1007/978-3-030-81455-7_23</a>.","ama":"Peitz S, Dellnitz M, Bannenberg S. Efficient Virtual Design and Testing of Autonomous Vehicles. In: Bock HG, Küfer K-H, Maas P, Milde A, Schulz V, eds. <i>German Success Stories in Industrial Mathematics</i>. Vol 35. Mathematics in Industry. Springer International Publishing; 2022. doi:<a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">10.1007/978-3-030-81455-7_23</a>","bibtex":"@inbook{Peitz_Dellnitz_Bannenberg_2022, place={Cham}, series={Mathematics in Industry}, title={Efficient Virtual Design and Testing of Autonomous Vehicles}, volume={35}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-81455-7_23\">10.1007/978-3-030-81455-7_23</a>}, booktitle={German Success Stories in Industrial Mathematics}, publisher={Springer International Publishing}, author={Peitz, Sebastian and Dellnitz, Michael and Bannenberg, Sebastian}, editor={Bock, H. G. and Küfer, K.-H. and Maas, P. and Milde, A. and Schulz, V.}, year={2022}, collection={Mathematics in Industry} }"},"editor":[{"full_name":"Bock, H. G.","first_name":"H. G.","last_name":"Bock"},{"last_name":"Küfer","first_name":"K.-H.","full_name":"Küfer, K.-H."},{"full_name":"Maas, P.","first_name":"P.","last_name":"Maas"},{"full_name":"Milde, A.","last_name":"Milde","first_name":"A."},{"first_name":"V.","last_name":"Schulz","full_name":"Schulz, V."}],"volume":35,"user_id":"47427","_id":"30294","publisher":"Springer International Publishing","status":"public"},{"user_id":"15694","volume":"14(1)","page":"57-89","language":[{"iso":"eng"}],"_id":"30490","date_updated":"2022-03-24T12:26:32Z","title":"Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations","status":"public","year":"2022","author":[{"last_name":"Cresson","first_name":"Jacky","full_name":"Cresson, Jacky"},{"first_name":"Fernando","last_name":"Jiménez","full_name":"Jiménez, Fernando"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"}],"type":"journal_article","department":[{"_id":"636"}],"date_created":"2022-03-24T12:26:10Z","publication":"AIMS","citation":{"bibtex":"@article{Cresson_Jiménez_Ober-Blöbaum_2022, title={Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations}, volume={14(1)}, journal={AIMS}, author={Cresson, Jacky and Jiménez, Fernando and Ober-Blöbaum, Sina}, year={2022}, pages={57–89} }","chicago":"Cresson, Jacky, Fernando Jiménez, and Sina Ober-Blöbaum. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” <i>AIMS</i> 14(1) (2022): 57–89.","short":"J. Cresson, F. Jiménez, S. Ober-Blöbaum, AIMS 14(1) (2022) 57–89.","ama":"Cresson J, Jiménez F, Ober-Blöbaum S. Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>. 2022;14(1):57-89.","ieee":"J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations,” <i>AIMS</i>, vol. 14(1), pp. 57–89, 2022.","apa":"Cresson, J., Jiménez, F., &#38; Ober-Blöbaum, S. (2022). Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>, <i>14(1)</i>, 57–89.","mla":"Cresson, Jacky, et al. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” <i>AIMS</i>, vol. 14(1), 2022, pp. 57–89."}},{"keyword":["Applied Mathematics","Management Science and Operations Research","Control and Optimization"],"type":"journal_article","department":[{"_id":"636"}],"date_created":"2022-04-08T17:23:13Z","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or <jats:italic>Fuller</jats:italic> phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the <jats:italic>turnpike</jats:italic> property. This property is further used in order to design simple and realistic suboptimal control strategies.</jats:p>"}],"publication":"Journal of Optimization Theory and Applications","citation":{"ieee":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike Property in Optimal Microbial Metabolite Production,” <i>Journal of Optimization Theory and Applications</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","apa":"Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., &#38; Pomet, J.-B. (2022). Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>","short":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal of Optimization Theory and Applications (2022).","chicago":"Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya, and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, 2022. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>.","mla":"Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","bibtex":"@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property in Optimal Microbial Metabolite Production}, DOI={<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>}, journal={Journal of Optimization Theory and Applications}, publisher={Springer Science and Business Media LLC}, author={Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}, year={2022} }","ama":"Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>"},"doi":"10.1007/s10957-022-02023-0","user_id":"87909","language":[{"iso":"eng"}],"_id":"30861","publisher":"Springer Science and Business Media LLC","date_updated":"2022-04-08T18:23:02Z","publication_status":"published","title":"Turnpike Property in Optimal Microbial Metabolite Production","status":"public","year":"2022","author":[{"full_name":"Caillau, Jean-Baptiste","first_name":"Jean-Baptiste","last_name":"Caillau"},{"last_name":"Djema","first_name":"Walid","full_name":"Djema, Walid"},{"full_name":"Gouzé, Jean-Luc","last_name":"Gouzé","first_name":"Jean-Luc"},{"id":"87909","first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya"},{"last_name":"Pomet","first_name":"Jean-Baptiste","full_name":"Pomet, Jean-Baptiste"}],"publication_identifier":{"issn":["0022-3239","1573-2878"]}},{"user_id":"70575","volume":229,"page":"303-394","_id":"31982","publisher":"Springer Science and Business Media LLC","status":"public","citation":{"bibtex":"@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>}, number={1}, journal={Inventiones mathematicae}, publisher={Springer Science and Business Media LLC}, author={Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}, year={2022}, pages={303–394} }","ama":"Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones mathematicae</i>. 2022;229(1):303-394. doi:<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>","mla":"Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones Mathematicae</i>, vol. 229, no. 1, Springer Science and Business Media LLC, 2022, pp. 303–94, doi:<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>.","short":"M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394.","chicago":"Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones Mathematicae</i> 229, no. 1 (2022): 303–94. <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">https://doi.org/10.1007/s00222-022-01108-x</a>.","ieee":"M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds,” <i>Inventiones mathematicae</i>, vol. 229, no. 1, pp. 303–394, 2022, doi: <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>.","apa":"Cekić, M., Delarue, B., Dyatlov, S., &#38; Paternain, G. P. (2022). The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones Mathematicae</i>, <i>229</i>(1), 303–394. <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">https://doi.org/10.1007/s00222-022-01108-x</a>"},"doi":"10.1007/s00222-022-01108-x","language":[{"iso":"eng"}],"date_updated":"2022-06-21T11:55:15Z","publication_status":"published","intvolume":"       229","title":"The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds","year":"2022","author":[{"first_name":"Mihajlo","last_name":"Cekić","full_name":"Cekić, Mihajlo"},{"id":"70575","full_name":"Delarue, Benjamin","first_name":"Benjamin","last_name":"Delarue"},{"last_name":"Dyatlov","first_name":"Semyon","full_name":"Dyatlov, Semyon"},{"last_name":"Paternain","first_name":"Gabriel P.","full_name":"Paternain, Gabriel P."}],"publication_identifier":{"issn":["0020-9910","1432-1297"]},"keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"548"}],"date_created":"2022-06-20T08:24:17Z","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with Betti number <jats:inline-formula><jats:alternatives><jats:tex-math>$$b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n                    <mml:mi>b</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:msub>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, the order of vanishing of the Ruelle zeta function at zero equals <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n                      <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, while in the hyperbolic case it is equal to <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-2b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n                    <mml:mn>2</mml:mn>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n                      <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>Σ</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with harmonic 1-forms on <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>"}],"publication":"Inventiones mathematicae","issue":"1"},{"place":"Frankfurt a. M.","date_created":"2022-06-28T06:30:12Z","type":"book_chapter","department":[{"_id":"98"},{"_id":"543"}],"publication":"Anfangsunterricht für alle Kinder - Willkommen in der Schule!","citation":{"ieee":"U. Häsel-Weide, M. Wallner, and M. Hattermann, “Symmetrieverständnis von Anfang an,” in <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>, M. Gutzmann, U. Carle, and Grundschulverband e. V., Eds. Frankfurt a. M., 2022, pp. 200–215.","apa":"Häsel-Weide, U., Wallner, M., &#38; Hattermann, M. (2022). Symmetrieverständnis von Anfang an. In M. Gutzmann, U. Carle, &#38; Grundschulverband e. V. (Eds.), <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i> (pp. 200–215).","mla":"Häsel-Weide, Uta, et al. “Symmetrieverständnis von Anfang an.” <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>, edited by M. Gutzmann et al., 2022, pp. 200–15.","bibtex":"@inbook{Häsel-Weide_Wallner_Hattermann_2022, place={Frankfurt a. M.}, title={Symmetrieverständnis von Anfang an}, booktitle={Anfangsunterricht für alle Kinder - Willkommen in der Schule!}, author={Häsel-Weide, Uta and Wallner, Melina and Hattermann, M.}, editor={Gutzmann, M. and Carle, U. and Grundschulverband e. V.}, year={2022}, pages={200–215} }","chicago":"Häsel-Weide, Uta, Melina Wallner, and M. Hattermann. “Symmetrieverständnis von Anfang an.” In <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>, edited by M. Gutzmann, U. Carle, and Grundschulverband e. V., 200–215. Frankfurt a. M., 2022.","ama":"Häsel-Weide U, Wallner M, Hattermann M. Symmetrieverständnis von Anfang an. In: Gutzmann M, Carle U, Grundschulverband e. V., eds. <i>Anfangsunterricht für alle Kinder - Willkommen in der Schule!</i>. ; 2022:200-215.","short":"U. Häsel-Weide, M. Wallner, M. Hattermann, in: M. Gutzmann, U. Carle, Grundschulverband e. V. (Eds.), Anfangsunterricht für alle Kinder - Willkommen in der Schule!, Frankfurt a. M., 2022, pp. 200–215."},"page":"200-215","language":[{"iso":"ger"}],"_id":"32233","user_id":"45445","editor":[{"full_name":"Gutzmann, M.","last_name":"Gutzmann","first_name":"M."},{"full_name":"Carle, U.","first_name":"U.","last_name":"Carle"}],"status":"public","title":"Symmetrieverständnis von Anfang an","year":"2022","corporate_editor":["Grundschulverband e. V."],"author":[{"id":"60267","first_name":"Uta","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta"},{"first_name":"Melina","last_name":"Wallner","full_name":"Wallner, Melina","id":"45445"},{"full_name":"Hattermann, M.","first_name":"M.","last_name":"Hattermann"}],"date_updated":"2022-07-05T06:48:40Z","publication_status":"published"},{"citation":{"ama":"Häsel-Weide U, Seitz S, Wallner M, Wilke Y. Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe. In: Lutz D, Becker J, Buchhaupt F, Katzenbach D, Strecker A, Urban M, eds. <i>Qualifizierung für Inklusion. Sekundarstufe</i>. Waxmann; 2022:83-100.","short":"U. Häsel-Weide, S. Seitz, M. Wallner, Y. Wilke, in: D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, M. Urban (Eds.), Qualifizierung für Inklusion. Sekundarstufe, Waxmann, Münster, 2022, pp. 83–100.","chicago":"Häsel-Weide, Uta, S. Seitz, Melina Wallner, and Y. Wilke. “Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe.” In <i>Qualifizierung für Inklusion. Sekundarstufe</i>, edited by D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, and M. Urban, 83–100. Münster: Waxmann, 2022.","bibtex":"@inbook{Häsel-Weide_Seitz_Wallner_Wilke_2022, place={Münster}, title={Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe}, booktitle={Qualifizierung für Inklusion. Sekundarstufe}, publisher={Waxmann}, author={Häsel-Weide, Uta and Seitz, S. and Wallner, Melina and Wilke, Y.}, editor={Lutz, D. and Becker, J. and Buchhaupt, F. and Katzenbach, D. and Strecker, A. and Urban, M.}, year={2022}, pages={83–100} }","mla":"Häsel-Weide, Uta, et al. “Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe.” <i>Qualifizierung für Inklusion. Sekundarstufe</i>, edited by D. Lutz et al., Waxmann, 2022, pp. 83–100.","apa":"Häsel-Weide, U., Seitz, S., Wallner, M., &#38; Wilke, Y. (2022). Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe. In D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, &#38; M. Urban (Eds.), <i>Qualifizierung für Inklusion. Sekundarstufe</i> (pp. 83–100). Waxmann.","ieee":"U. Häsel-Weide, S. Seitz, M. Wallner, and Y. Wilke, “Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe,” in <i>Qualifizierung für Inklusion. Sekundarstufe</i>, D. Lutz, J. Becker, F. Buchhaupt, D. Katzenbach, A. Strecker, and M. Urban, Eds. Münster: Waxmann, 2022, pp. 83–100."},"publication":"Qualifizierung für Inklusion. Sekundarstufe","department":[{"_id":"98"},{"_id":"543"}],"type":"book_chapter","date_created":"2022-07-11T05:31:28Z","place":"Münster","publication_status":"published","date_updated":"2022-07-11T05:31:46Z","author":[{"id":"60267","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","first_name":"Uta"},{"full_name":"Seitz, S.","first_name":"S.","last_name":"Seitz"},{"id":"45445","last_name":"Wallner","first_name":"Melina","full_name":"Wallner, Melina"},{"full_name":"Wilke, Y.","last_name":"Wilke","first_name":"Y."}],"status":"public","title":"Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe","year":"2022","editor":[{"full_name":"Lutz, D.","last_name":"Lutz","first_name":"D."},{"first_name":"J.","last_name":"Becker","full_name":"Becker, J."},{"full_name":"Buchhaupt, F.","last_name":"Buchhaupt","first_name":"F."},{"last_name":"Katzenbach","first_name":"D.","full_name":"Katzenbach, D."},{"full_name":"Strecker, A.","last_name":"Strecker","first_name":"A."},{"full_name":"Urban, M.","last_name":"Urban","first_name":"M."}],"user_id":"85821","_id":"32339","publisher":"Waxmann","language":[{"iso":"ger"}],"page":"83-100"},{"related_material":{"link":[{"relation":"contains","url":"https://doi.org/10.21248/qfi.72"}]},"issue":"2","publication":"QfI - Qualifizierung für Inklusion","citation":{"ieee":"K. Hähn, U. Häsel-Weide, and P. Scherer, “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.,” <i>QfI - Qualifizierung für Inklusion</i>, vol. 3, no. 2, 2022.","apa":"Hähn, K., Häsel-Weide, U., &#38; Scherer, P. (2022). Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. <i>QfI - Qualifizierung für Inklusion</i>, <i>3</i>(2).","short":"K. Hähn, U. Häsel-Weide, P. Scherer, QfI - Qualifizierung für Inklusion 3 (2022).","chicago":"Hähn, K., Uta Häsel-Weide, and P. Scherer. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.” <i>QfI - Qualifizierung für Inklusion</i> 3, no. 2 (2022).","mla":"Hähn, K., et al. “Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.” <i>QfI - Qualifizierung für Inklusion</i>, vol. 3, no. 2, 2022.","bibtex":"@article{Hähn_Häsel-Weide_Scherer_2022, title={Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.}, volume={3}, number={2}, journal={QfI - Qualifizierung für Inklusion}, author={Hähn, K. and Häsel-Weide, Uta and Scherer, P.}, year={2022} }","ama":"Hähn K, Häsel-Weide U, Scherer P. Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. <i>QfI - Qualifizierung für Inklusion</i>. 2022;3(2)."},"type":"journal_article","department":[{"_id":"98"},{"_id":"543"}],"date_created":"2022-07-11T05:13:52Z","date_updated":"2022-07-11T05:31:41Z","publication_status":"published","intvolume":"         3","year":"2022","title":"Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.","status":"public","author":[{"full_name":"Hähn, K.","first_name":"K.","last_name":"Hähn"},{"id":"60267","last_name":"Häsel-Weide","first_name":"Uta","full_name":"Häsel-Weide, Uta"},{"last_name":"Scherer","first_name":"P.","full_name":"Scherer, P."}],"user_id":"85821","volume":3,"_id":"32338","language":[{"iso":"ger"}]},{"citation":{"mla":"Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, IOP Publishing Ltd., 2022, p. 314002, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","ama":"Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(31):314002. doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>","bibtex":"@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems}, volume={55}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>}, number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}, year={2022}, pages={314002} }","apa":"Klus, S., Nüske, F., &#38; Peitz, S. (2022). Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(31), 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>","ieee":"S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, p. 314002, 2022, doi: <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","short":"S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical 55 (2022) 314002.","chicago":"Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55, no. 31 (2022): 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>."},"oa":"1","external_id":{"arxiv":["2201.12062"]},"status":"public","volume":55,"user_id":"47427","publisher":"IOP Publishing Ltd.","_id":"29673","page":"314002","abstract":[{"lang":"eng","text":"Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson's stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science."}],"issue":"31","publication":"Journal of Physics A: Mathematical and Theoretical","department":[{"_id":"655"},{"_id":"101"}],"type":"journal_article","date_created":"2022-01-31T09:49:40Z","intvolume":"        55","publication_status":"published","date_updated":"2022-07-18T14:26:41Z","author":[{"full_name":"Klus, Stefan","first_name":"Stefan","last_name":"Klus"},{"id":"81513","last_name":"Nüske","first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian","last_name":"Peitz","id":"47427"}],"year":"2022","title":"Koopman analysis of quantum systems","doi":"10.1088/1751-8121/ac7d22","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf"}]}]