[{"publication":"arXiv:2603.26949","type":"preprint","status":"public","abstract":[{"text":"In this paper we generalize the geodesic flow on (finite) homogeneous graphs to a multiparameter flow on compact quotients of Euclidean buildings. Then we study the joint spectra of the associated transfer operators acting on suitable Lipschitz spaces. The main result says that outside an arbitrarily small neighborhood of zero in the set of spectral parameters the Taylor spectrum of the commuting family of transfer operators is contained in the joint point spectrum.","lang":"eng"}],"user_id":"220","external_id":{"arxiv":["2603.26949"]},"_id":"65255","language":[{"iso":"eng"}],"citation":{"ama":"Hilgert J, Kahl D, Weich T. Spectral theory for transfer operators on compact quotients of Euclidean buildings. <i>arXiv:260326949</i>. Published online 2026.","ieee":"J. Hilgert, D. Kahl, and T. Weich, “Spectral theory for transfer operators on compact quotients of Euclidean buildings,” <i>arXiv:2603.26949</i>. 2026.","chicago":"Hilgert, Joachim, Daniel Kahl, and Tobias Weich. “Spectral Theory for Transfer Operators on Compact Quotients of Euclidean Buildings.” <i>ArXiv:2603.26949</i>, 2026.","apa":"Hilgert, J., Kahl, D., &#38; Weich, T. (2026). Spectral theory for transfer operators on compact quotients of Euclidean buildings. In <i>arXiv:2603.26949</i>.","bibtex":"@article{Hilgert_Kahl_Weich_2026, title={Spectral theory for transfer operators on compact quotients of Euclidean buildings}, journal={arXiv:2603.26949}, author={Hilgert, Joachim and Kahl, Daniel and Weich, Tobias}, year={2026} }","short":"J. Hilgert, D. Kahl, T. Weich, ArXiv:2603.26949 (2026).","mla":"Hilgert, Joachim, et al. “Spectral Theory for Transfer Operators on Compact Quotients of Euclidean Buildings.” <i>ArXiv:2603.26949</i>, 2026."},"year":"2026","author":[{"last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220","first_name":"Joachim"},{"first_name":"Daniel","last_name":"Kahl","full_name":"Kahl, Daniel","id":"55661"},{"id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias"}],"date_created":"2026-03-31T08:30:34Z","date_updated":"2026-03-31T08:31:01Z","title":"Spectral theory for transfer operators on compact quotients of Euclidean buildings"},{"user_id":"220","_id":"58402","language":[{"iso":"eng"}],"article_number":"21","type":"journal_article","publication":"Analysis and Mathematical Physics","status":"public","author":[{"first_name":"Thomas","last_name":"Baier","full_name":"Baier, Thomas"},{"full_name":"Ferreira, Ana Cristina","last_name":"Ferreira","first_name":"Ana Cristina"},{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"},{"first_name":"José M.","last_name":"Mourão","full_name":"Mourão, José M."},{"last_name":"Nunes","full_name":"Nunes, João P.","first_name":"João P."}],"date_created":"2025-01-30T07:45:52Z","volume":15,"date_updated":"2025-01-30T07:46:30Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s13324-025-01012-6","title":"Fibering polarizations and Mabuchi rays on symmetric spaces of compact type","issue":"1","publication_status":"published","publication_identifier":{"issn":["1664-2368","1664-235X"]},"citation":{"apa":"Baier, T., Ferreira, A. C., Hilgert, J., Mourão, J. M., &#38; Nunes, J. P. (2025). Fibering polarizations and Mabuchi rays on symmetric spaces of compact type. <i>Analysis and Mathematical Physics</i>, <i>15</i>(1), Article 21. <a href=\"https://doi.org/10.1007/s13324-025-01012-6\">https://doi.org/10.1007/s13324-025-01012-6</a>","mla":"Baier, Thomas, et al. “Fibering Polarizations and Mabuchi Rays on Symmetric Spaces of Compact Type.” <i>Analysis and Mathematical Physics</i>, vol. 15, no. 1, 21, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s13324-025-01012-6\">10.1007/s13324-025-01012-6</a>.","bibtex":"@article{Baier_Ferreira_Hilgert_Mourão_Nunes_2025, title={Fibering polarizations and Mabuchi rays on symmetric spaces of compact type}, volume={15}, DOI={<a href=\"https://doi.org/10.1007/s13324-025-01012-6\">10.1007/s13324-025-01012-6</a>}, number={121}, journal={Analysis and Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Baier, Thomas and Ferreira, Ana Cristina and Hilgert, Joachim and Mourão, José M. and Nunes, João P.}, year={2025} }","short":"T. Baier, A.C. Ferreira, J. Hilgert, J.M. Mourão, J.P. Nunes, Analysis and Mathematical Physics 15 (2025).","ama":"Baier T, Ferreira AC, Hilgert J, Mourão JM, Nunes JP. Fibering polarizations and Mabuchi rays on symmetric spaces of compact type. <i>Analysis and Mathematical Physics</i>. 2025;15(1). doi:<a href=\"https://doi.org/10.1007/s13324-025-01012-6\">10.1007/s13324-025-01012-6</a>","ieee":"T. Baier, A. C. Ferreira, J. Hilgert, J. M. Mourão, and J. P. Nunes, “Fibering polarizations and Mabuchi rays on symmetric spaces of compact type,” <i>Analysis and Mathematical Physics</i>, vol. 15, no. 1, Art. no. 21, 2025, doi: <a href=\"https://doi.org/10.1007/s13324-025-01012-6\">10.1007/s13324-025-01012-6</a>.","chicago":"Baier, Thomas, Ana Cristina Ferreira, Joachim Hilgert, José M. Mourão, and João P. Nunes. “Fibering Polarizations and Mabuchi Rays on Symmetric Spaces of Compact Type.” <i>Analysis and Mathematical Physics</i> 15, no. 1 (2025). <a href=\"https://doi.org/10.1007/s13324-025-01012-6\">https://doi.org/10.1007/s13324-025-01012-6</a>."},"intvolume":"        15","year":"2025"},{"year":"2025","citation":{"ama":"Arends C, Frahm J, Hilgert J. Edge Laplacians and Edge Poisson Transforms for Graphs. <i>Potential Analysis</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1007/s11118-024-10184-y\">10.1007/s11118-024-10184-y</a>","chicago":"Arends, Christian, Jan Frahm, and Joachim Hilgert. “Edge Laplacians and Edge Poisson Transforms for Graphs.” <i>Potential Analysis</i>, 2025. <a href=\"https://doi.org/10.1007/s11118-024-10184-y\">https://doi.org/10.1007/s11118-024-10184-y</a>.","ieee":"C. Arends, J. Frahm, and J. Hilgert, “Edge Laplacians and Edge Poisson Transforms for Graphs,” <i>Potential Analysis</i>, 2025, doi: <a href=\"https://doi.org/10.1007/s11118-024-10184-y\">10.1007/s11118-024-10184-y</a>.","short":"C. Arends, J. Frahm, J. Hilgert, Potential Analysis (2025).","bibtex":"@article{Arends_Frahm_Hilgert_2025, title={Edge Laplacians and Edge Poisson Transforms for Graphs}, DOI={<a href=\"https://doi.org/10.1007/s11118-024-10184-y\">10.1007/s11118-024-10184-y</a>}, journal={Potential Analysis}, publisher={Springer Science and Business Media LLC}, author={Arends, Christian and Frahm, Jan and Hilgert, Joachim}, year={2025} }","mla":"Arends, Christian, et al. “Edge Laplacians and Edge Poisson Transforms for Graphs.” <i>Potential Analysis</i>, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s11118-024-10184-y\">10.1007/s11118-024-10184-y</a>.","apa":"Arends, C., Frahm, J., &#38; Hilgert, J. (2025). Edge Laplacians and Edge Poisson Transforms for Graphs. <i>Potential Analysis</i>. <a href=\"https://doi.org/10.1007/s11118-024-10184-y\">https://doi.org/10.1007/s11118-024-10184-y</a>"},"publication_status":"published","publication_identifier":{"issn":["0926-2601","1572-929X"]},"title":"Edge Laplacians and Edge Poisson Transforms for Graphs","doi":"10.1007/s11118-024-10184-y","date_updated":"2025-04-04T08:02:34Z","publisher":"Springer Science and Business Media LLC","date_created":"2025-04-04T08:02:14Z","author":[{"first_name":"Christian","full_name":"Arends, Christian","last_name":"Arends"},{"first_name":"Jan","full_name":"Frahm, Jan","last_name":"Frahm"},{"first_name":"Joachim","full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert"}],"abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>For a finite graph, we establish natural isomorphisms between eigenspaces of a Laplace operator acting on functions on the edges and eigenspaces of a transfer operator acting on functions on one-sided infinite non-backtracking paths. Interpreting the transfer operator as a classical dynamical system and the Laplace operator as its quantization, this result can be viewed as a <jats:italic>quantum-classical correspondence</jats:italic>. In contrast to previously established quantum-classical correspondences for the vertex Laplacian which exclude certain exceptional spectral parameters, our correspondence is valid for all parameters. This allows us to relate certain spectral quantities to topological properties of the graph such as the cyclomatic number and the 2-colorability. The quantum-classical correspondence for the edge Laplacian is induced by an edge Poisson transform on the universal covering of the graph which is a tree of bounded degree. In the special case of regular trees, we relate both the vertex and the edge Poisson transform to the representation theory of the automorphism group of the tree and study associated operator valued Hecke algebras.</jats:p>","lang":"eng"}],"status":"public","type":"journal_article","publication":"Potential Analysis","language":[{"iso":"eng"}],"_id":"59344","user_id":"220"},{"language":[{"iso":"eng"}],"user_id":"220","_id":"59343","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>On a finite regular graph, (co)resonant states are eigendistributions of the transfer operator associated to the shift on one-sided infinite non-backtracking paths. We introduce two pairings of resonant and coresonant states, the <jats:italic>vertex pairing</jats:italic> which involves only the dependence on the initial/terminal vertex of the path, and the <jats:italic>geodesic pairing</jats:italic> which is given by integrating over all geodesics the evaluation of the coresonant state on the first half of the geodesic times the resonant state on the second half. The main result is that these two pairings coincide up to a constant which depends on the resonance, i.e. the corresponding eigenvalue of the transfer operator.</jats:p>","lang":"eng"}],"publication":"Mathematische Annalen","type":"journal_article","doi":"10.1007/s00208-025-03140-7","title":"A pairing formula for resonant states on finite regular graphs","date_created":"2025-04-04T07:59:29Z","author":[{"last_name":"Arends","full_name":"Arends, Christian","first_name":"Christian"},{"first_name":"Jan","last_name":"Frahm","full_name":"Frahm, Jan"},{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"}],"publisher":"Springer Science and Business Media LLC","date_updated":"2025-04-04T07:59:58Z","citation":{"chicago":"Arends, Christian, Jan Frahm, and Joachim Hilgert. “A Pairing Formula for Resonant States on Finite Regular Graphs.” <i>Mathematische Annalen</i>, 2025. <a href=\"https://doi.org/10.1007/s00208-025-03140-7\">https://doi.org/10.1007/s00208-025-03140-7</a>.","ieee":"C. Arends, J. Frahm, and J. Hilgert, “A pairing formula for resonant states on finite regular graphs,” <i>Mathematische Annalen</i>, 2025, doi: <a href=\"https://doi.org/10.1007/s00208-025-03140-7\">10.1007/s00208-025-03140-7</a>.","ama":"Arends C, Frahm J, Hilgert J. A pairing formula for resonant states on finite regular graphs. <i>Mathematische Annalen</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1007/s00208-025-03140-7\">10.1007/s00208-025-03140-7</a>","apa":"Arends, C., Frahm, J., &#38; Hilgert, J. (2025). A pairing formula for resonant states on finite regular graphs. <i>Mathematische Annalen</i>. <a href=\"https://doi.org/10.1007/s00208-025-03140-7\">https://doi.org/10.1007/s00208-025-03140-7</a>","bibtex":"@article{Arends_Frahm_Hilgert_2025, title={A pairing formula for resonant states on finite regular graphs}, DOI={<a href=\"https://doi.org/10.1007/s00208-025-03140-7\">10.1007/s00208-025-03140-7</a>}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Arends, Christian and Frahm, Jan and Hilgert, Joachim}, year={2025} }","mla":"Arends, Christian, et al. “A Pairing Formula for Resonant States on Finite Regular Graphs.” <i>Mathematische Annalen</i>, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00208-025-03140-7\">10.1007/s00208-025-03140-7</a>.","short":"C. Arends, J. Frahm, J. Hilgert, Mathematische Annalen (2025)."},"year":"2025","publication_identifier":{"issn":["0025-5831","1432-1807"]},"publication_status":"published"},{"user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"64736","language":[{"iso":"eng"}],"type":"journal_editor","publication":"J. Lie Theory","status":"public","editor":[{"first_name":"Jan","last_name":"Frahm","full_name":"Frahm, Jan"},{"first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178"},{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"},{"last_name":"Olafsson","full_name":"Olafsson, Gestur","first_name":"Gestur"}],"date_created":"2026-02-26T17:42:01Z","volume":35,"date_updated":"2026-02-26T17:51:43Z","title":"Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday","issue":"4","quality_controlled":"1","citation":{"apa":"Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday. (2025). In J. Frahm, H. Glöckner, J. Hilgert, &#38; G. Olafsson (Eds.), <i>J. Lie Theory</i> (Vol. 35, Issue 4).","short":"J. Frahm, H. Glöckner, J. Hilgert, G. Olafsson, eds., Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday, 2025.","bibtex":"@book{Frahm_Glöckner_Hilgert_Olafsson_2025, title={Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday}, volume={35}, number={4}, journal={J. Lie Theory}, year={2025} }","mla":"Frahm, Jan, et al., editors. “Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday.” <i>J. Lie Theory</i>, vol. 35, no. 4, 2025.","chicago":"Frahm, Jan, Helge Glöckner, Joachim Hilgert, and Gestur Olafsson, eds. <i>Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday</i>. <i>J. Lie Theory</i>. Vol. 35, 2025.","ieee":"J. Frahm, H. Glöckner, J. Hilgert, and G. Olafsson, Eds., <i>Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday</i>, vol. 35, no. 4. 2025.","ama":"Frahm J, Glöckner H, Hilgert J, Olafsson G, eds. <i>Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday</i>. Vol 35.; 2025."},"intvolume":"        35","year":"2025"},{"title":"Quantum-Classical Correspondences for Locally Symmetric Spaces","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-981-97-7662-7_7"}],"doi":"https://doi.org/10.1007/978-981-97-7662-7","date_updated":"2025-02-11T18:10:35Z","date_created":"2025-02-11T17:59:07Z","author":[{"full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert","first_name":"Joachim"}],"year":"2025","citation":{"ama":"Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces. In: <i>Symmetry in Geometry and Analysis, Volume 2</i>. ; 2025. doi:<a href=\"https://doi.org/10.1007/978-981-97-7662-7\">https://doi.org/10.1007/978-981-97-7662-7</a>","ieee":"J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces,” in <i>Symmetry in Geometry and Analysis, Volume 2</i>, 2025.","chicago":"Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric Spaces.” In <i>Symmetry in Geometry and Analysis, Volume 2</i>, 2025. <a href=\"https://doi.org/10.1007/978-981-97-7662-7\">https://doi.org/10.1007/978-981-97-7662-7</a>.","apa":"Hilgert, J. (2025). Quantum-Classical Correspondences for Locally Symmetric Spaces. In <i>Symmetry in Geometry and Analysis, Volume 2</i>. <a href=\"https://doi.org/10.1007/978-981-97-7662-7\">https://doi.org/10.1007/978-981-97-7662-7</a>","mla":"Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric Spaces.” <i>Symmetry in Geometry and Analysis, Volume 2</i>, 2025, doi:<a href=\"https://doi.org/10.1007/978-981-97-7662-7\">https://doi.org/10.1007/978-981-97-7662-7</a>.","bibtex":"@inbook{Hilgert_2025, title={Quantum-Classical Correspondences for Locally Symmetric Spaces}, DOI={<a href=\"https://doi.org/10.1007/978-981-97-7662-7\">https://doi.org/10.1007/978-981-97-7662-7</a>}, booktitle={Symmetry in Geometry and Analysis, Volume 2}, author={Hilgert, Joachim}, year={2025} }","short":"J. Hilgert, in: Symmetry in Geometry and Analysis, Volume 2, 2025."},"language":[{"iso":"eng"}],"_id":"58587","user_id":"220","status":"public","type":"book_chapter","publication":"Symmetry in Geometry and Analysis, Volume 2"},{"year":"2025","citation":{"ieee":"B. Delarue and J. Hilgert, “Quantum resonances and scattering poles of classical rank one locally  symmetric spaces,” <i>Journal of Lie Theory</i>, vol. 35, no. (4), pp. 787--804.","chicago":"Delarue, Benjamin, and Joachim Hilgert. “Quantum Resonances and Scattering Poles of Classical Rank One Locally  Symmetric Spaces.” <i>Journal of Lie Theory</i> 35, no. (4) (n.d.): 787--804.","ama":"Delarue B, Hilgert J. Quantum resonances and scattering poles of classical rank one locally  symmetric spaces. <i>Journal of Lie Theory</i>. 35((4)):787--804.","apa":"Delarue, B., &#38; Hilgert, J. (n.d.). Quantum resonances and scattering poles of classical rank one locally  symmetric spaces. <i>Journal of Lie Theory</i>, <i>35</i>((4)), 787--804.","bibtex":"@article{Delarue_Hilgert, title={Quantum resonances and scattering poles of classical rank one locally  symmetric spaces}, volume={35}, number={(4)}, journal={Journal of Lie Theory}, author={Delarue, Benjamin and Hilgert, Joachim}, pages={787--804} }","mla":"Delarue, Benjamin, and Joachim Hilgert. “Quantum Resonances and Scattering Poles of Classical Rank One Locally  Symmetric Spaces.” <i>Journal of Lie Theory</i>, vol. 35, no. (4), pp. 787--804.","short":"B. Delarue, J. Hilgert, Journal of Lie Theory 35 (n.d.) 787--804."},"page":"787--804","intvolume":"        35","publication_status":"inpress","publication_identifier":{"issn":["0949-5932"]},"issue":"(4)","title":"Quantum resonances and scattering poles of classical rank one locally  symmetric spaces","date_updated":"2026-03-31T09:07:17Z","date_created":"2024-04-11T12:31:18Z","author":[{"last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin","first_name":"Benjamin"},{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"}],"volume":35,"abstract":[{"lang":"eng","text":"For negatively curved symmetric spaces it is known that the poles of the\r\nscattering matrices defined via the standard intertwining operators for the\r\nspherical principal representations of the isometry group are either given as\r\npoles of the intertwining operators or as quantum resonances, i.e. poles of the\r\nmeromorphically continued resolvents of the Laplace-Beltrami operator. We\r\nextend this result to classical locally symmetric spaces of negative curvature\r\nwith convex-cocompact fundamental group using results of Bunke and Olbrich. The\r\nmethod of proof forces us to exclude the spectral parameters corresponding to\r\nsingular Poisson transforms."}],"status":"public","type":"journal_article","publication":"Journal of Lie Theory","article_type":"original","language":[{"iso":"eng"}],"_id":"53413","user_id":"220","department":[{"_id":"548"}]},{"year":"2024","place":"Berlin, Heidelberg","citation":{"short":"M. Hoffmann, J. Hilgert, T. Weich, Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik, Springer Berlin Heidelberg, Berlin, Heidelberg, 2024.","bibtex":"@book{Hoffmann_Hilgert_Weich_2024, place={Berlin, Heidelberg}, title={Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>}, publisher={Springer Berlin Heidelberg}, author={Hoffmann, Max and Hilgert, Joachim and Weich, Tobias}, year={2024} }","mla":"Hoffmann, Max, et al. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg, 2024, doi:<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>.","apa":"Hoffmann, M., Hilgert, J., &#38; Weich, T. (2024). <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-67357-7\">https://doi.org/10.1007/978-3-662-67357-7</a>","chicago":"Hoffmann, Max, Joachim Hilgert, and Tobias Weich. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. <a href=\"https://doi.org/10.1007/978-3-662-67357-7\">https://doi.org/10.1007/978-3-662-67357-7</a>.","ieee":"M. Hoffmann, J. Hilgert, and T. Weich, <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024.","ama":"Hoffmann M, Hilgert J, Weich T. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg; 2024. doi:<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>"},"publication_status":"published","publication_identifier":{"isbn":["9783662673560","9783662673577"]},"title":"Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik","doi":"10.1007/978-3-662-67357-7","publisher":"Springer Berlin Heidelberg","date_updated":"2024-08-08T08:05:30Z","date_created":"2024-07-12T08:36:42Z","author":[{"first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max","id":"32202"},{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"},{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias"}],"status":"public","type":"book","language":[{"iso":"ger"}],"_id":"55193","user_id":"220","department":[{"_id":"97"},{"_id":"643"},{"_id":"548"}]},{"status":"public","type":"book","alternative_title":["From Linear Algebra over Rings to Geometry with Sheaves"],"language":[{"iso":"eng"}],"user_id":"220","_id":"60078","citation":{"short":"J. Hilgert, Mathematical Structures, Springer Berlin Heidelberg, Berlin, Heidelberg, 2024.","bibtex":"@book{Hilgert_2024, place={Berlin, Heidelberg}, title={Mathematical Structures}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-69412-1\">10.1007/978-3-662-69412-1</a>}, publisher={Springer Berlin Heidelberg}, author={Hilgert, Joachim}, year={2024} }","mla":"Hilgert, Joachim. <i>Mathematical Structures</i>. Springer Berlin Heidelberg, 2024, doi:<a href=\"https://doi.org/10.1007/978-3-662-69412-1\">10.1007/978-3-662-69412-1</a>.","ama":"Hilgert J. <i>Mathematical Structures</i>. Springer Berlin Heidelberg; 2024. doi:<a href=\"https://doi.org/10.1007/978-3-662-69412-1\">10.1007/978-3-662-69412-1</a>","apa":"Hilgert, J. (2024). <i>Mathematical Structures</i>. Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-69412-1\">https://doi.org/10.1007/978-3-662-69412-1</a>","chicago":"Hilgert, Joachim. <i>Mathematical Structures</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. <a href=\"https://doi.org/10.1007/978-3-662-69412-1\">https://doi.org/10.1007/978-3-662-69412-1</a>.","ieee":"J. Hilgert, <i>Mathematical Structures</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024."},"year":"2024","place":"Berlin, Heidelberg","publication_status":"published","publication_identifier":{"issn":["2731-3824","2731-3832"],"isbn":["9783662694114","9783662694121"]},"doi":"10.1007/978-3-662-69412-1","title":"Mathematical Structures","date_created":"2025-05-30T16:11:49Z","author":[{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"}],"publisher":"Springer Berlin Heidelberg","date_updated":"2025-05-30T16:12:23Z"},{"language":[{"iso":"eng"}],"ddc":["510"],"publication":"J. Europ. Math. Soc.","file":[{"file_id":"32102","file_name":"2007.14275.pdf","access_level":"open_access","file_size":796410,"creator":"weich","date_created":"2022-06-22T09:56:47Z","date_updated":"2022-06-22T09:56:47Z","relation":"main_file","content_type":"application/pdf"}],"date_created":"2022-06-22T09:56:51Z","title":"Ruelle-Taylor resonances of Anosov actions","issue":"8","year":"2024","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"_id":"32101","file_date_updated":"2022-06-22T09:56:47Z","type":"journal_article","status":"public","author":[{"last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"},{"first_name":"Yannick","full_name":"Guedes Bonthonneau, Yannick","last_name":"Guedes Bonthonneau"},{"full_name":"Guillarmou, Colin","last_name":"Guillarmou","first_name":"Colin"},{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"}],"volume":27,"date_updated":"2026-02-18T10:33:34Z","oa":"1","doi":"https://doi.org/10.4171/JEMS/1428","publication_status":"published","has_accepted_license":"1","citation":{"short":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. 27 (2024) 3085–3147.","mla":"Weich, Tobias, et al. “Ruelle-Taylor Resonances of Anosov Actions.” <i>J. Europ. Math. Soc.</i>, vol. 27, no. 8, 2024, pp. 3085–3147, doi:<a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>.","bibtex":"@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor resonances of Anosov actions}, volume={27}, DOI={<a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>}, number={8}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024}, pages={3085–3147} }","apa":"Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., &#38; Hilgert, J. (2024). Ruelle-Taylor resonances of Anosov actions. <i>J. Europ. Math. Soc.</i>, <i>27</i>(8), 3085–3147. <a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>","ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonances of Anosov actions. <i>J Europ Math Soc</i>. 2024;27(8):3085–3147. doi:<a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>","ieee":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor resonances of Anosov actions,” <i>J. Europ. Math. Soc.</i>, vol. 27, no. 8, pp. 3085–3147, 2024, doi: <a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>.","chicago":"Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim Hilgert. “Ruelle-Taylor Resonances of Anosov Actions.” <i>J. Europ. Math. Soc.</i> 27, no. 8 (2024): 3085–3147. <a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>."},"page":"3085–3147","intvolume":"        27"},{"type":"journal_article","publication":"Journal of Geometry and Physics","status":"public","_id":"57498","user_id":"220","article_number":"105355","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0393-0440"]},"year":"2024","citation":{"apa":"Baier, T., Hilgert, J., Kaya, O., Mourão, J. M., &#38; Nunes, J. P. (2024). Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem. <i>Journal of Geometry and Physics</i>, <i>207</i>, Article 105355. <a href=\"https://doi.org/10.1016/j.geomphys.2024.105355\">https://doi.org/10.1016/j.geomphys.2024.105355</a>","short":"T. Baier, J. Hilgert, O. Kaya, J.M. Mourão, J.P. Nunes, Journal of Geometry and Physics 207 (2024).","mla":"Baier, Thomas, et al. “Quantization in Fibering Polarizations, Mabuchi Rays and Geometric Peter–Weyl Theorem.” <i>Journal of Geometry and Physics</i>, vol. 207, 105355, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.geomphys.2024.105355\">10.1016/j.geomphys.2024.105355</a>.","bibtex":"@article{Baier_Hilgert_Kaya_Mourão_Nunes_2024, title={Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem}, volume={207}, DOI={<a href=\"https://doi.org/10.1016/j.geomphys.2024.105355\">10.1016/j.geomphys.2024.105355</a>}, number={105355}, journal={Journal of Geometry and Physics}, publisher={Elsevier BV}, author={Baier, Thomas and Hilgert, Joachim and Kaya, Oguzhan and Mourão, José M. and Nunes, João P.}, year={2024} }","ama":"Baier T, Hilgert J, Kaya O, Mourão JM, Nunes JP. Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem. <i>Journal of Geometry and Physics</i>. 2024;207. doi:<a href=\"https://doi.org/10.1016/j.geomphys.2024.105355\">10.1016/j.geomphys.2024.105355</a>","chicago":"Baier, Thomas, Joachim Hilgert, Oguzhan Kaya, José M. Mourão, and João P. Nunes. “Quantization in Fibering Polarizations, Mabuchi Rays and Geometric Peter–Weyl Theorem.” <i>Journal of Geometry and Physics</i> 207 (2024). <a href=\"https://doi.org/10.1016/j.geomphys.2024.105355\">https://doi.org/10.1016/j.geomphys.2024.105355</a>.","ieee":"T. Baier, J. Hilgert, O. Kaya, J. M. Mourão, and J. P. Nunes, “Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem,” <i>Journal of Geometry and Physics</i>, vol. 207, Art. no. 105355, 2024, doi: <a href=\"https://doi.org/10.1016/j.geomphys.2024.105355\">10.1016/j.geomphys.2024.105355</a>."},"intvolume":"       207","date_updated":"2025-01-13T15:57:19Z","publisher":"Elsevier BV","author":[{"first_name":"Thomas","last_name":"Baier","full_name":"Baier, Thomas"},{"last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220","first_name":"Joachim"},{"full_name":"Kaya, Oguzhan","last_name":"Kaya","first_name":"Oguzhan"},{"first_name":"José M.","full_name":"Mourão, José M.","last_name":"Mourão"},{"first_name":"João P.","full_name":"Nunes, João P.","last_name":"Nunes"}],"date_created":"2024-11-29T09:45:57Z","volume":207,"title":"Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem","doi":"10.1016/j.geomphys.2024.105355"},{"author":[{"first_name":"K.-U.","full_name":"Bux, K.-U.","last_name":"Bux"},{"last_name":"Hilgert","id":"220","full_name":"Hilgert, Joachim","first_name":"Joachim"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"}],"date_created":"2025-01-08T09:39:58Z","volume":36,"date_updated":"2025-01-13T16:00:06Z","publisher":"Elsevier BV","doi":"10.1016/j.indag.2024.05.001","title":"Spectral correspondences for finite graphs without dead ends","issue":"1","publication_status":"published","publication_identifier":{"issn":["0019-3577"]},"citation":{"short":"K.-U. Bux, J. Hilgert, T. Weich, Indagationes Mathematicae 36 (2024) 188–217.","mla":"Bux, K. U., et al. “Spectral Correspondences for Finite Graphs without Dead Ends.” <i>Indagationes Mathematicae</i>, vol. 36, no. 1, Elsevier BV, 2024, pp. 188–217, doi:<a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">10.1016/j.indag.2024.05.001</a>.","bibtex":"@article{Bux_Hilgert_Weich_2024, title={Spectral correspondences for finite graphs without dead ends}, volume={36}, DOI={<a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">10.1016/j.indag.2024.05.001</a>}, number={1}, journal={Indagationes Mathematicae}, publisher={Elsevier BV}, author={Bux, K.-U. and Hilgert, Joachim and Weich, Tobias}, year={2024}, pages={188–217} }","apa":"Bux, K.-U., Hilgert, J., &#38; Weich, T. (2024). Spectral correspondences for finite graphs without dead ends. <i>Indagationes Mathematicae</i>, <i>36</i>(1), 188–217. <a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">https://doi.org/10.1016/j.indag.2024.05.001</a>","chicago":"Bux, K.-U., Joachim Hilgert, and Tobias Weich. “Spectral Correspondences for Finite Graphs without Dead Ends.” <i>Indagationes Mathematicae</i> 36, no. 1 (2024): 188–217. <a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">https://doi.org/10.1016/j.indag.2024.05.001</a>.","ieee":"K.-U. Bux, J. Hilgert, and T. Weich, “Spectral correspondences for finite graphs without dead ends,” <i>Indagationes Mathematicae</i>, vol. 36, no. 1, pp. 188–217, 2024, doi: <a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">10.1016/j.indag.2024.05.001</a>.","ama":"Bux K-U, Hilgert J, Weich T. Spectral correspondences for finite graphs without dead ends. <i>Indagationes Mathematicae</i>. 2024;36(1):188-217. doi:<a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">10.1016/j.indag.2024.05.001</a>"},"page":"188-217","intvolume":"        36","year":"2024","user_id":"220","_id":"58103","language":[{"iso":"eng"}],"type":"journal_article","publication":"Indagationes Mathematicae","status":"public"},{"doi":"10.1007/978-3-662-68893-9","title":"Mathematische Strukturen 2. Auflage","date_created":"2024-12-05T09:09:58Z","author":[{"full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert","first_name":"Joachim"}],"date_updated":"2025-01-13T16:08:17Z","publisher":"Springer Berlin Heidelberg","citation":{"apa":"Hilgert, J. (2024). <i>Mathematische Strukturen 2. Auflage</i>. Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-68893-9\">https://doi.org/10.1007/978-3-662-68893-9</a>","short":"J. Hilgert, Mathematische Strukturen 2. Auflage, Springer Berlin Heidelberg, Berlin, Heidelberg, 2024.","mla":"Hilgert, Joachim. <i>Mathematische Strukturen 2. Auflage</i>. Springer Berlin Heidelberg, 2024, doi:<a href=\"https://doi.org/10.1007/978-3-662-68893-9\">10.1007/978-3-662-68893-9</a>.","bibtex":"@book{Hilgert_2024, place={Berlin, Heidelberg}, title={Mathematische Strukturen 2. Auflage}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-68893-9\">10.1007/978-3-662-68893-9</a>}, publisher={Springer Berlin Heidelberg}, author={Hilgert, Joachim}, year={2024} }","ama":"Hilgert J. <i>Mathematische Strukturen 2. Auflage</i>. Springer Berlin Heidelberg; 2024. doi:<a href=\"https://doi.org/10.1007/978-3-662-68893-9\">10.1007/978-3-662-68893-9</a>","ieee":"J. Hilgert, <i>Mathematische Strukturen 2. Auflage</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024.","chicago":"Hilgert, Joachim. <i>Mathematische Strukturen 2. Auflage</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. <a href=\"https://doi.org/10.1007/978-3-662-68893-9\">https://doi.org/10.1007/978-3-662-68893-9</a>."},"year":"2024","place":"Berlin, Heidelberg","publication_status":"published","publication_identifier":{"isbn":["9783662688922","9783662688939"]},"alternative_title":["Von der linearen Algebra über Ringen zur Geometrie mit Garben"],"language":[{"iso":"ger"}],"user_id":"220","_id":"57590","status":"public","type":"book"},{"year":"2023","title":"Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters","date_created":"2022-05-11T12:27:00Z","abstract":[{"text":"In this paper we complete the program of relating the Laplace spectrum for\r\nrank one compact locally symmetric spaces with the first band Ruelle-Pollicott\r\nresonances of the geodesic flow on its sphere bundle. This program was started\r\nby Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and\r\nGuillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for\r\ngeneral rank one spaces. Except for the case of hyperbolic surfaces a countable\r\nset of exceptional spectral parameters always left untreated since the\r\ncorresponding Poisson transforms are neither injective nor surjective. We use\r\nvector valued Poisson transforms to treat also the exceptional spectral\r\nparameters. For surfaces the exceptional spectral parameters lead to discrete\r\nseries representations of $\\mathrm{SL}(2,\\mathbb R)$. In higher dimensions the\r\nsituation is more complicated, but can be described completely.","lang":"eng"}],"publication":"Journal de l’École polytechnique — Mathématiques","language":[{"iso":"eng"}],"keyword":["Ruelle resonances","Poisson transforms","locally symmetric spaces","principal series representations"],"external_id":{"arxiv":["2112.11073"]},"citation":{"chicago":"Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” <i>Journal de l’École Polytechnique — Mathématiques</i> 10 (2023): 335–403. <a href=\"https://doi.org/10.5802/jep.220\">https://doi.org/10.5802/jep.220</a>.","ieee":"C. Arends and J. Hilgert, “Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters,” <i>Journal de l’École polytechnique — Mathématiques</i>, vol. 10, pp. 335–403, 2023, doi: <a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>.","ama":"Arends C, Hilgert J. Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. <i>Journal de l’École polytechnique — Mathématiques</i>. 2023;10:335-403. doi:<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>","bibtex":"@article{Arends_Hilgert_2023, title={Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters}, volume={10}, DOI={<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>}, journal={Journal de l’École polytechnique — Mathématiques}, author={Arends, Christian and Hilgert, Joachim}, year={2023}, pages={335–403} }","short":"C. Arends, J. Hilgert, Journal de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","mla":"Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” <i>Journal de l’École Polytechnique — Mathématiques</i>, vol. 10, 2023, pp. 335–403, doi:<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>.","apa":"Arends, C., &#38; Hilgert, J. (2023). Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. <i>Journal de l’École Polytechnique — Mathématiques</i>, <i>10</i>, 335–403. <a href=\"https://doi.org/10.5802/jep.220\">https://doi.org/10.5802/jep.220</a>"},"intvolume":"        10","page":"335-403","publication_status":"published","publication_identifier":{"issn":["2429-7100"],"eissn":["2270-518X"]},"doi":"10.5802/jep.220","author":[{"last_name":"Arends","full_name":"Arends, Christian","id":"43994","first_name":"Christian"},{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"}],"volume":10,"date_updated":"2024-02-19T06:30:26Z","status":"public","type":"journal_article","user_id":"49063","department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"_id":"31210"},{"user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"},{"_id":"91"}],"_id":"34793","article_type":"original","type":"journal_article","status":"public","author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"},{"full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert","first_name":"Joachim"}],"volume":343,"date_updated":"2024-03-22T16:02:32Z","doi":"10.1016/j.jde.2022.10.001","publication_identifier":{"issn":["0022-0396"]},"citation":{"chicago":"Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” <i>Journal of Differential Equations</i> 343 (2023): 186–232. <a href=\"https://doi.org/10.1016/j.jde.2022.10.001\">https://doi.org/10.1016/j.jde.2022.10.001</a>.","ieee":"H. Glöckner and J. Hilgert, “Aspects of control theory on infinite-dimensional Lie groups and G-manifolds,” <i>Journal of Differential Equations</i>, vol. 343, pp. 186–232, 2023, doi: <a href=\"https://doi.org/10.1016/j.jde.2022.10.001\">10.1016/j.jde.2022.10.001</a>.","ama":"Glöckner H, Hilgert J. Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. <i>Journal of Differential Equations</i>. 2023;343:186–232. doi:<a href=\"https://doi.org/10.1016/j.jde.2022.10.001\">10.1016/j.jde.2022.10.001</a>","apa":"Glöckner, H., &#38; Hilgert, J. (2023). Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. <i>Journal of Differential Equations</i>, <i>343</i>, 186–232. <a href=\"https://doi.org/10.1016/j.jde.2022.10.001\">https://doi.org/10.1016/j.jde.2022.10.001</a>","bibtex":"@article{Glöckner_Hilgert_2023, title={Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}, volume={343}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2022.10.001\">10.1016/j.jde.2022.10.001</a>}, journal={Journal of Differential Equations}, author={Glöckner, Helge and Hilgert, Joachim}, year={2023}, pages={186–232} }","mla":"Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” <i>Journal of Differential Equations</i>, vol. 343, 2023, pp. 186–232, doi:<a href=\"https://doi.org/10.1016/j.jde.2022.10.001\">10.1016/j.jde.2022.10.001</a>.","short":"H. Glöckner, J. Hilgert, Journal of Differential Equations 343 (2023) 186–232."},"intvolume":"       343","page":"186–232","external_id":{"arxiv":["2007.11277"]},"language":[{"iso":"eng"}],"keyword":["22E65","28B05","34A12","34H05","46E30","46E40"],"publication":"Journal of Differential Equations","date_created":"2022-12-21T19:31:13Z","title":"Aspects of control theory on infinite-dimensional Lie groups and G-manifolds","quality_controlled":"1","year":"2023"},{"language":[{"iso":"eng"}],"external_id":{"arxiv":["2103.05667"]},"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"}],"publication":"Analysis & PDE","title":"Higher rank quantum-classical correspondence","date_created":"2022-05-11T10:41:35Z","publisher":"MSP","year":"2023","issue":"10","user_id":"49178","department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"_id":"31190","status":"public","type":"journal_article","doi":"https://doi.org/10.2140/apde.2023.16.2241","author":[{"first_name":"Joachim","full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"first_name":"Lasse Lennart","orcid":"0000-0001-8893-2045","last_name":"Wolf","id":"45027","full_name":"Wolf, Lasse Lennart"}],"volume":16,"date_updated":"2026-02-18T10:39:36Z","citation":{"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>","short":"J. Hilgert, T. Weich, L.L. Wolf, Analysis &#38; PDE 16 (2023) 2241–2265.","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>.","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>","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>.","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>."},"page":"2241–2265","intvolume":"        16"},{"title":"Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters","date_updated":"2026-03-31T08:26:09Z","volume":10,"date_created":"2024-02-19T06:34:11Z","author":[{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"},{"last_name":"Arends","full_name":"Arends, C.","first_name":"C."}],"year":"2023","page":"335-403","intvolume":"        10","citation":{"short":"J. Hilgert, C. Arends, J. de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","mla":"Hilgert, Joachim, and C. 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In <i>Mathematische Semesterberichte</i> (Vol. 69, pp. 151–153). <a href=\"https://doi.org/10.1007/s00591-021-00314-7\">https://doi.org/10.1007/s00591-021-00314-7</a>","mla":"Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021.” <i>Mathematische Semesterberichte</i>, vol. 69, 2022, pp. 151–153, doi:<a href=\"https://doi.org/10.1007/s00591-021-00314-7\">10.1007/s00591-021-00314-7</a>.","short":"J. Hilgert, Mathematische Semesterberichte 69 (2022) 151–153.","bibtex":"@article{Hilgert_2022, title={Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021}, volume={69}, DOI={<a href=\"https://doi.org/10.1007/s00591-021-00314-7\">10.1007/s00591-021-00314-7</a>}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2022}, pages={151–153} }"},"publication_status":"published","title":"Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. 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