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