{"publication_identifier":{"eissn":["2270-518X"],"issn":["2429-7100"]},"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"}],"_id":"31210","date_updated":"2024-02-19T06:30:26Z","doi":"10.5802/jep.220","publication":"Journal de l’École polytechnique — Mathématiques","title":"Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters","status":"public","keyword":["Ruelle resonances","Poisson transforms","locally symmetric spaces","principal series representations"],"type":"journal_article","user_id":"49063","publication_status":"published","page":"335-403","volume":10,"language":[{"iso":"eng"}],"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>.","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>","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>.","short":"C. Arends, J. Hilgert, Journal de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","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} }"},"intvolume":"        10","author":[{"id":"43994","last_name":"Arends","full_name":"Arends, Christian","first_name":"Christian"},{"id":"220","last_name":"Hilgert","full_name":"Hilgert, Joachim","first_name":"Joachim"}],"department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"year":"2023","date_created":"2022-05-11T12:27:00Z","external_id":{"arxiv":["2112.11073"]}}