[{"citation":{"bibtex":"@article{Olbrich_Palmirotta_2026, title={Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond}, volume={299}, DOI={<a href=\"https://doi.org/10.1002/mana.70100\">10.1002/mana.70100</a>}, number={2}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2026}, pages={456–479} }","ama":"Olbrich M, Palmirotta G. Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond. <i>Mathematische Nachrichten</i>. 2026;299(2):456-479. doi:<a href=\"https://doi.org/10.1002/mana.70100\">10.1002/mana.70100</a>","mla":"Olbrich, Martin, and Guendalina Palmirotta. “Solvability of Invariant Systems of Differential Equations on H2$\\mathbb {H}^2$ and Beyond.” <i>Mathematische Nachrichten</i>, vol. 299, no. 2, Wiley, 2026, pp. 456–79, doi:<a href=\"https://doi.org/10.1002/mana.70100\">10.1002/mana.70100</a>.","chicago":"Olbrich, Martin, and Guendalina Palmirotta. “Solvability of Invariant Systems of Differential Equations on H2$\\mathbb {H}^2$ and Beyond.” <i>Mathematische Nachrichten</i> 299, no. 2 (2026): 456–79. <a href=\"https://doi.org/10.1002/mana.70100\">https://doi.org/10.1002/mana.70100</a>.","short":"M. Olbrich, G. Palmirotta, Mathematische Nachrichten 299 (2026) 456–479.","ieee":"M. Olbrich and G. Palmirotta, “Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond,” <i>Mathematische Nachrichten</i>, vol. 299, no. 2, pp. 456–479, 2026, doi: <a href=\"https://doi.org/10.1002/mana.70100\">10.1002/mana.70100</a>.","apa":"Olbrich, M., &#38; Palmirotta, G. (2026). Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond. <i>Mathematische Nachrichten</i>, <i>299</i>(2), 456–479. <a href=\"https://doi.org/10.1002/mana.70100\">https://doi.org/10.1002/mana.70100</a>"},"page":"456-479","publisher":"Wiley","_id":"64569","user_id":"109467","volume":299,"status":"public","date_created":"2026-02-20T19:56:33Z","type":"journal_article","department":[{"_id":"548"}],"publication":"Mathematische Nachrichten","issue":"2","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n                  <jats:p>We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non‐compact type  can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander's proof of the Ehrenpreis–Malgrange theorem. We get complete solvability for the hyperbolic plane  and partial results for products  and the hyperbolic 3‐space .</jats:p>"}],"language":[{"iso":"eng"}],"doi":"10.1002/mana.70100","title":"Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond","year":"2026","author":[{"last_name":"Olbrich","first_name":"Martin","full_name":"Olbrich, Martin"},{"first_name":"Guendalina","last_name":"Palmirotta","full_name":"Palmirotta, Guendalina","id":"109467"}],"publication_identifier":{"issn":["0025-584X","1522-2616"]},"date_updated":"2026-02-20T20:01:56Z","publication_status":"published","intvolume":"       299"},{"publication":"Journal of Differential Equations","related_material":{"link":[{"relation":"confirmation","url":"https://www.sciencedirect.com/science/article/pii/S0022039625010927?via%3Dihub"}]},"abstract":[{"lang":"eng","text":"We investigate dispersive and Strichartz estimates for the Schrödinger equation involving the fractional Laplacian in real hyperbolic spaces and their discrete analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives. A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears on homogeneous trees, due to the triviality of the estimates for small times."}],"date_created":"2024-12-04T16:21:38Z","department":[{"_id":"10"},{"_id":"548"}],"keyword":["Schrödinger equation","Fractional Laplacian","Dispersive estimates","Strichartz estimates","Real hyperbolic spaces","Homogeneous trees"],"type":"journal_article","author":[{"full_name":"Palmirotta, Guendalina","last_name":"Palmirotta","first_name":"Guendalina","id":"109467"},{"full_name":"Sire, Yannick","first_name":"Yannick","last_name":"Sire"},{"full_name":"Anker, Jean-Philippe","last_name":"Anker","first_name":"Jean-Philippe"}],"year":"2026","title":"The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees","publication_status":"published","date_updated":"2026-03-30T12:03:37Z","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jde.2025.114065"}],"doi":"10.1016/j.jde.2025.114065","citation":{"chicago":"Palmirotta, Guendalina, Yannick Sire, and Jean-Philippe Anker. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” <i>Journal of Differential Equations</i>, 2026. <a href=\"https://doi.org/10.1016/j.jde.2025.114065\">https://doi.org/10.1016/j.jde.2025.114065</a>.","short":"G. Palmirotta, Y. Sire, J.-P. Anker, Journal of Differential Equations (2026).","ama":"Palmirotta G, Sire Y, Anker J-P. The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. <i>Journal of Differential Equations</i>. Published online 2026. doi:<a href=\"https://doi.org/10.1016/j.jde.2025.114065\">10.1016/j.jde.2025.114065</a>","bibtex":"@article{Palmirotta_Sire_Anker_2026, title={The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2025.114065\">10.1016/j.jde.2025.114065</a>}, journal={Journal of Differential Equations}, publisher={Elsevier}, author={Palmirotta, Guendalina and Sire, Yannick and Anker, Jean-Philippe}, year={2026} }","mla":"Palmirotta, Guendalina, et al. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” <i>Journal of Differential Equations</i>, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.jde.2025.114065\">10.1016/j.jde.2025.114065</a>.","apa":"Palmirotta, G., Sire, Y., &#38; Anker, J.-P. (2026). The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. <i>Journal of Differential Equations</i>. <a href=\"https://doi.org/10.1016/j.jde.2025.114065\">https://doi.org/10.1016/j.jde.2025.114065</a>","ieee":"G. Palmirotta, Y. Sire, and J.-P. Anker, “The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees,” <i>Journal of Differential Equations</i>, 2026, doi: <a href=\"https://doi.org/10.1016/j.jde.2025.114065\">10.1016/j.jde.2025.114065</a>."},"project":[{"_id":"356","name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)"}],"external_id":{"arxiv":["2412.00780"]},"oa":"1","status":"public","_id":"57580","publisher":"Elsevier","user_id":"109467"},{"title":"Patterson-Sullivan distributions of finite regular graphs","status":"public","year":"2026","author":[{"full_name":"Arends, Christian","last_name":"Arends","first_name":"Christian"},{"full_name":"Palmirotta, Guendalina","last_name":"Palmirotta","first_name":"Guendalina","id":"109467"}],"date_updated":"2026-03-30T12:02:56Z","page":"38","main_file_link":[{"url":"https://arxiv.org/abs/2603.09779","open_access":"1"}],"language":[{"iso":"eng"}],"_id":"65232","user_id":"109467","publication":"arXiv:2603.09779","citation":{"mla":"Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions of Finite Regular Graphs.” <i>ArXiv:2603.09779</i>, 2026.","ama":"Arends C, Palmirotta G. Patterson-Sullivan distributions of finite regular graphs. <i>arXiv:260309779</i>. Published online 2026.","bibtex":"@article{Arends_Palmirotta_2026, title={Patterson-Sullivan distributions of finite regular graphs}, journal={arXiv:2603.09779}, author={Arends, Christian and Palmirotta, Guendalina}, year={2026} }","apa":"Arends, C., &#38; Palmirotta, G. (2026). Patterson-Sullivan distributions of finite regular graphs. In <i>arXiv:2603.09779</i>.","ieee":"C. Arends and G. Palmirotta, “Patterson-Sullivan distributions of finite regular graphs,” <i>arXiv:2603.09779</i>. 2026.","short":"C. Arends, G. Palmirotta, ArXiv:2603.09779 (2026).","chicago":"Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions of Finite Regular Graphs.” <i>ArXiv:2603.09779</i>, 2026."},"abstract":[{"lang":"eng","text":"On finite regular graphs, we construct Patterson-Sullivan distributions associated with eigenfunctions of the discrete Laplace operator via their boundary values on the phase space. These distributions are closely related to Wigner distributions defined via a pseudo-differential calculus on graphs, which appear naturally in the study of quantum chaos. Using a pairing formula, we prove that Patterson-Sullivan distributions are also related to invariant Ruelle distributions arising from the transfer operator of the geodesic flow on the shift space. Both relationships provide discrete analogues of results for compact hyperbolic surfaces obtained by Anantharaman-Zelditch and by Guillarmou-Hilgert-Weich."}],"project":[{"name":"TRR 358; TP B04:  Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden","_id":"358"}],"external_id":{"arxiv":["2603.09779"]},"date_created":"2026-03-30T11:56:04Z","type":"preprint","oa":"1","department":[{"_id":"548"},{"_id":"10"},{"_id":"34"}]},{"citation":{"short":"G. Palmirotta, (2026).","chicago":"Palmirotta, Guendalina. “Residues of Weighted Dynamical Ihara Zeta Functions on Finite Regular Graphs,” 2026.","ieee":"G. Palmirotta, “Residues of weighted dynamical Ihara zeta functions on finite regular graphs.” 2026.","apa":"Palmirotta, G. (2026). <i>Residues of weighted dynamical Ihara zeta functions on finite regular graphs</i>.","bibtex":"@article{Palmirotta_2026, title={Residues of weighted dynamical Ihara zeta functions on finite regular graphs}, author={Palmirotta, Guendalina}, year={2026} }","ama":"Palmirotta G. Residues of weighted dynamical Ihara zeta functions on finite regular graphs. Published online 2026.","mla":"Palmirotta, Guendalina. <i>Residues of Weighted Dynamical Ihara Zeta Functions on Finite Regular Graphs</i>. 2026."},"abstract":[{"lang":"eng","text":"A weighted dynamical version $\\mathbf{Z}_f$ of the classical Ihara zeta function is presented on connected finite regular graphs, expressed in terms of weighted periodic orbit data. We establish its meromorphic continuation, with poles given by the resonances of the associated non-backtracking transfer operator acting on a suitable Banach space, and compute its residues. At simple spectral parameters, the residue of $\\mathbf{Z}_f$ is identified with the invariant Ruelle distribution on the graph phase space. Combining this result with a relation obtained by Arends-Palmirotta, we further derive Patterson-Sullivan and Wigner residue formulae. This provides a finite-graph analogue of residue formulae for weighted dynamical zeta functions for geodesic flow on rank one locally symmetric spaces, in the spirit of Schütte-Barkhofen-Weich."}],"date_created":"2026-09-14T07:49:06Z","type":"preprint","department":[{"_id":"548"},{"_id":"10"},{"_id":"34"}],"status":"public","year":"2026","title":"Residues of weighted dynamical Ihara zeta functions on finite regular graphs","author":[{"id":"109467","full_name":"Palmirotta, Guendalina","first_name":"Guendalina","last_name":"Palmirotta"}],"date_updated":"2026-09-14T07:51:03Z","page":"53","language":[{"iso":"eng"}],"_id":"67136","user_id":"109467"},{"type":"preprint","department":[{"_id":"548"}],"external_id":{"arxiv":["2411.19782"]},"date_created":"2025-02-28T10:32:30Z","abstract":[{"lang":"eng","text":"We prove that the Patterson-Sullivan and Wigner distributions on the unit\r\nsphere bundle of a convex-cocompact hyperbolic surface are asymptotically\r\nidentical. This generalizes results in the compact case by\r\nAnantharaman-Zelditch and Hansen-Hilgert-Schr\\\"oder."}],"project":[{"_id":"356","name":"TRR 358; TP B02: Spektraltheorie in höherem Rang und unendlichem Volumen"}],"publication":"arXiv:2411.19782","citation":{"bibtex":"@article{Delarue_Palmirotta_2024, title={Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces}, journal={arXiv:2411.19782}, author={Delarue, Benjamin and Palmirotta, Guendalina}, year={2024} }","ama":"Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. <i>arXiv:241119782</i>. Published online 2024.","mla":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","chicago":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","short":"B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).","ieee":"B. Delarue and G. Palmirotta, “Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces,” <i>arXiv:2411.19782</i>. 2024.","apa":"Delarue, B., &#38; Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. In <i>arXiv:2411.19782</i>."},"user_id":"109467","language":[{"iso":"eng"}],"_id":"58873","date_updated":"2026-03-30T12:01:12Z","title":"Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces","year":"2024","status":"public","author":[{"id":"70575","last_name":"Delarue","first_name":"Benjamin","full_name":"Delarue, Benjamin"},{"last_name":"Palmirotta","first_name":"Guendalina","full_name":"Palmirotta, Guendalina","id":"109467"}]},{"volume":63,"user_id":"109467","_id":"64570","publisher":"Springer Science and Business Media LLC","status":"public","citation":{"ama":"Olbrich M, Palmirotta G. Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces. <i>Annals of Global Analysis and Geometry</i>. 2022;63(1). doi:<a href=\"https://doi.org/10.1007/s10455-022-09882-w\">10.1007/s10455-022-09882-w</a>","bibtex":"@article{Olbrich_Palmirotta_2022, title={Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces}, volume={63}, DOI={<a href=\"https://doi.org/10.1007/s10455-022-09882-w\">10.1007/s10455-022-09882-w</a>}, number={19}, journal={Annals of Global Analysis and Geometry}, publisher={Springer Science and Business Media LLC}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2022} }","mla":"Olbrich, Martin, and Guendalina Palmirotta. “Delorme’s Intertwining Conditions for Sections of Homogeneous Vector Bundles on Two- and Three-Dimensional Hyperbolic Spaces.” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 1, 9, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10455-022-09882-w\">10.1007/s10455-022-09882-w</a>.","chicago":"Olbrich, Martin, and Guendalina Palmirotta. “Delorme’s Intertwining Conditions for Sections of Homogeneous Vector Bundles on Two- and Three-Dimensional Hyperbolic Spaces.” <i>Annals of Global Analysis and Geometry</i> 63, no. 1 (2022). <a href=\"https://doi.org/10.1007/s10455-022-09882-w\">https://doi.org/10.1007/s10455-022-09882-w</a>.","short":"M. Olbrich, G. Palmirotta, Annals of Global Analysis and Geometry 63 (2022).","apa":"Olbrich, M., &#38; Palmirotta, G. (2022). Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces. <i>Annals of Global Analysis and Geometry</i>, <i>63</i>(1), Article 9. <a href=\"https://doi.org/10.1007/s10455-022-09882-w\">https://doi.org/10.1007/s10455-022-09882-w</a>","ieee":"M. Olbrich and G. Palmirotta, “Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces,” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 1, Art. no. 9, 2022, doi: <a href=\"https://doi.org/10.1007/s10455-022-09882-w\">10.1007/s10455-022-09882-w</a>."},"doi":"10.1007/s10455-022-09882-w","language":[{"iso":"eng"}],"article_number":"9","intvolume":"        63","date_updated":"2026-02-20T20:03:38Z","publication_status":"published","author":[{"last_name":"Olbrich","first_name":"Martin","full_name":"Olbrich, Martin"},{"id":"109467","full_name":"Palmirotta, Guendalina","last_name":"Palmirotta","first_name":"Guendalina"}],"publication_identifier":{"issn":["0232-704X","1572-9060"]},"title":"Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces","year":"2022","department":[{"_id":"10"},{"_id":"548"}],"type":"journal_article","date_created":"2026-02-20T20:02:50Z","extern":"1","publication":"Annals of Global Analysis and Geometry","issue":"1"},{"author":[{"full_name":"Olbrich, Martin","last_name":"Olbrich","first_name":"Martin"},{"first_name":"Guendalina","last_name":"Palmirotta","full_name":"Palmirotta, Guendalina","id":"109467"}],"year":"2022","title":"A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$","intvolume":"        34","date_updated":"2026-02-20T20:07:31Z","publication_status":"published","language":[{"iso":"eng"}],"publication":"Journal of Lie theory","issue":"2","abstract":[{"lang":"eng","text":"We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type $X = G/K$. We prove a characterisation of their range. In fact, from Delorme's Paley-Wiener theorem for compactly supported smooth functions on a real reductive group of Harish-Chandra class, we deduce topological Paley-Wiener and Paley-Wiener-Schwartz theorems for sections."}],"extern":"1","date_created":"2026-02-20T20:04:49Z","department":[{"_id":"10"},{"_id":"548"}],"type":"journal_article","status":"public","_id":"64571","publisher":"Heldermann Verlag","page":"53--384","volume":34,"user_id":"109467","citation":{"mla":"Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” <i>Journal of Lie Theory</i>, vol. 34, no. 2, Heldermann Verlag, 2022, pp. 53--384.","ama":"Olbrich M, Palmirotta G. A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$. <i>Journal of Lie theory</i>. 2022;34(2):53--384.","bibtex":"@article{Olbrich_Palmirotta_2022, title={A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$}, volume={34}, number={2}, journal={Journal of Lie theory}, publisher={Heldermann Verlag}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2022}, pages={53--384} }","apa":"Olbrich, M., &#38; Palmirotta, G. (2022). A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$. <i>Journal of Lie Theory</i>, <i>34</i>(2), 53--384.","ieee":"M. Olbrich and G. Palmirotta, “A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$,” <i>Journal of Lie theory</i>, vol. 34, no. 2, pp. 53--384, 2022.","short":"M. Olbrich, G. Palmirotta, Journal of Lie Theory 34 (2022) 53--384.","chicago":"Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” <i>Journal of Lie Theory</i> 34, no. 2 (2022): 53--384."},"external_id":{"arxiv":["2202.06905"]}}]