[{"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."}],"publication":"Journal of Differential Equations","keyword":["Schrödinger equation","Fractional Laplacian","Dispersive estimates","Strichartz estimates","Real hyperbolic spaces","Homogeneous trees"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2412.00780"]},"year":"2026","title":"The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees","publisher":"Elsevier","date_created":"2024-12-04T16:21:38Z","status":"public","type":"journal_article","_id":"57580","project":[{"name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)","_id":"356"}],"department":[{"_id":"10"},{"_id":"548"}],"user_id":"109467","citation":{"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>","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>","short":"G. Palmirotta, Y. Sire, J.-P. Anker, Journal of Differential Equations (2026).","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>.","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>.","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>."},"publication_status":"published","related_material":{"link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0022039625010927?via%3Dihub","relation":"confirmation"}]},"doi":"10.1016/j.jde.2025.114065","main_file_link":[{"url":"https://doi.org/10.1016/j.jde.2025.114065","open_access":"1"}],"oa":"1","date_updated":"2026-03-30T12:03:37Z","author":[{"first_name":"Guendalina","last_name":"Palmirotta","id":"109467","full_name":"Palmirotta, Guendalina"},{"first_name":"Yannick","last_name":"Sire","full_name":"Sire, Yannick"},{"first_name":"Jean-Philippe","last_name":"Anker","full_name":"Anker, Jean-Philippe"}]},{"_id":"32099","project":[{"name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)","_id":"356","grant_number":"491392403"},{"grant_number":"422642921","name":"Mikrolokale Methoden für hyperbolische Dynamiken","_id":"355"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","file_date_updated":"2022-06-22T09:56:39Z","type":"journal_article","status":"public","oa":"1","date_updated":"2024-09-25T08:18:44Z","volume":288,"author":[{"first_name":"Tobias","full_name":"Weich, Tobias","id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich"},{"full_name":"Budde, Julia","last_name":"Budde","first_name":"Julia"}],"doi":" https://doi.org/10.1016/j.jfa.2024.110684","has_accepted_license":"1","intvolume":"       288","citation":{"short":"T. Weich, J. Budde, Journal of Functional Analysis 288 (2025).","bibtex":"@article{Weich_Budde_2025, title={Wave Front Sets of Nilpotent Lie Group Representations}, volume={288}, DOI={<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>}, number={1}, journal={Journal of Functional Analysis}, author={Weich, Tobias and Budde, Julia}, year={2025} }","mla":"Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.” <i>Journal of Functional Analysis</i>, vol. 288, no. 1, 2025, doi:<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>.","apa":"Weich, T., &#38; Budde, J. (2025). Wave Front Sets of Nilpotent Lie Group Representations. <i>Journal of Functional Analysis</i>, <i>288</i>(1). <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\">https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684</a>","chicago":"Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.” <i>Journal of Functional Analysis</i> 288, no. 1 (2025). <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\">https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684</a>.","ieee":"T. Weich and J. Budde, “Wave Front Sets of Nilpotent Lie Group Representations,” <i>Journal of Functional Analysis</i>, vol. 288, no. 1, 2025, doi: <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>.","ama":"Weich T, Budde J. Wave Front Sets of Nilpotent Lie Group Representations. <i>Journal of Functional Analysis</i>. 2025;288(1). doi:<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>"},"ddc":["510"],"language":[{"iso":"eng"}],"publication":"Journal of Functional Analysis","file":[{"content_type":"application/pdf","relation":"main_file","date_updated":"2022-06-22T09:56:39Z","date_created":"2022-06-22T09:56:39Z","creator":"weich","file_size":978990,"file_name":"2103.02968.pdf","file_id":"32100","access_level":"open_access"}],"date_created":"2022-06-22T09:56:43Z","title":"Wave Front Sets of Nilpotent Lie Group Representations","issue":"1","year":"2025"},{"type":"preprint","publication":"arXiv:2411.19782","abstract":[{"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.","lang":"eng"}],"status":"public","project":[{"name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)","_id":"356","grant_number":"491392403"}],"external_id":{"arxiv":["2411.19782"]},"_id":"57582","user_id":"109467","department":[{"_id":"10"},{"_id":"548"}],"language":[{"iso":"eng"}],"year":"2024","citation":{"chicago":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","ieee":"B. Delarue and G. Palmirotta, “Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces,” <i>arXiv:2411.19782</i>. 2024.","ama":"Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. <i>arXiv:241119782</i>. Published online 2024.","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} }","mla":"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).","apa":"Delarue, B., &#38; Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. In <i>arXiv:2411.19782</i>."},"date_updated":"2024-12-04T16:33:27Z","author":[{"full_name":"Delarue, Benjamin","last_name":"Delarue","first_name":"Benjamin"},{"full_name":"Palmirotta, Guendalina","last_name":"Palmirotta","first_name":"Guendalina"}],"date_created":"2024-12-04T16:28:05Z","title":"Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces"},{"language":[{"iso":"eng"}],"department":[{"_id":"548"}],"user_id":"109467","external_id":{"arxiv":["2411.19782"]},"_id":"58873","project":[{"name":"TRR 358; TP B02: Spektraltheorie in höherem Rang und unendlichem Volumen","_id":"356"}],"status":"public","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."}],"publication":"arXiv:2411.19782","type":"preprint","title":"Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces","date_created":"2025-02-28T10:32:30Z","author":[{"last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin","first_name":"Benjamin"},{"id":"109467","full_name":"Palmirotta, Guendalina","last_name":"Palmirotta","first_name":"Guendalina"}],"date_updated":"2026-03-30T12:01:12Z","citation":{"apa":"Delarue, B., &#38; Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. In <i>arXiv:2411.19782</i>.","short":"B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).","mla":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","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} }","ieee":"B. Delarue and G. 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.","ama":"Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. <i>arXiv:241119782</i>. Published online 2024."},"year":"2024"}]