---
_id: '52876'
article_number: L012043
author:
- first_name: Christian
  full_name: Arends, Christian
  id: '43994'
  last_name: Arends
- first_name: Lasse Lennart
  full_name: Wolf, Lasse Lennart
  id: '45027'
  last_name: Wolf
  orcid: 0000-0001-8893-2045
- first_name: Jasmin
  full_name: Meinecke, Jasmin
  last_name: Meinecke
- first_name: Sonja
  full_name: Barkhofen, Sonja
  id: '48188'
  last_name: Barkhofen
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Tim
  full_name: Bartley, Tim
  id: '49683'
  last_name: Bartley
citation:
  ama: Arends C, Wolf LL, Meinecke J, Barkhofen S, Weich T, Bartley T. Decomposing
    large unitaries into multimode devices of arbitrary size. <i>Physical Review Research</i>.
    2024;6(1). doi:<a href="https://doi.org/10.1103/physrevresearch.6.l012043">10.1103/physrevresearch.6.l012043</a>
  apa: Arends, C., Wolf, L. L., Meinecke, J., Barkhofen, S., Weich, T., &#38; Bartley,
    T. (2024). Decomposing large unitaries into multimode devices of arbitrary size.
    <i>Physical Review Research</i>, <i>6</i>(1), Article L012043. <a href="https://doi.org/10.1103/physrevresearch.6.l012043">https://doi.org/10.1103/physrevresearch.6.l012043</a>
  bibtex: '@article{Arends_Wolf_Meinecke_Barkhofen_Weich_Bartley_2024, title={Decomposing
    large unitaries into multimode devices of arbitrary size}, volume={6}, DOI={<a
    href="https://doi.org/10.1103/physrevresearch.6.l012043">10.1103/physrevresearch.6.l012043</a>},
    number={1L012043}, journal={Physical Review Research}, publisher={American Physical
    Society (APS)}, author={Arends, Christian and Wolf, Lasse Lennart and Meinecke,
    Jasmin and Barkhofen, Sonja and Weich, Tobias and Bartley, Tim}, year={2024} }'
  chicago: Arends, Christian, Lasse Lennart Wolf, Jasmin Meinecke, Sonja Barkhofen,
    Tobias Weich, and Tim Bartley. “Decomposing Large Unitaries into Multimode Devices
    of Arbitrary Size.” <i>Physical Review Research</i> 6, no. 1 (2024). <a href="https://doi.org/10.1103/physrevresearch.6.l012043">https://doi.org/10.1103/physrevresearch.6.l012043</a>.
  ieee: 'C. Arends, L. L. Wolf, J. Meinecke, S. Barkhofen, T. Weich, and T. Bartley,
    “Decomposing large unitaries into multimode devices of arbitrary size,” <i>Physical
    Review Research</i>, vol. 6, no. 1, Art. no. L012043, 2024, doi: <a href="https://doi.org/10.1103/physrevresearch.6.l012043">10.1103/physrevresearch.6.l012043</a>.'
  mla: Arends, Christian, et al. “Decomposing Large Unitaries into Multimode Devices
    of Arbitrary Size.” <i>Physical Review Research</i>, vol. 6, no. 1, L012043, American
    Physical Society (APS), 2024, doi:<a href="https://doi.org/10.1103/physrevresearch.6.l012043">10.1103/physrevresearch.6.l012043</a>.
  short: C. Arends, L.L. Wolf, J. Meinecke, S. Barkhofen, T. Weich, T. Bartley, Physical
    Review Research 6 (2024).
date_created: 2024-03-26T08:52:05Z
date_updated: 2025-12-04T13:38:49Z
department:
- _id: '623'
- _id: '15'
doi: 10.1103/physrevresearch.6.l012043
intvolume: '         6'
issue: '1'
keyword:
- General Physics and Astronomy
language:
- iso: eng
publication: Physical Review Research
publication_identifier:
  issn:
  - 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Decomposing large unitaries into multimode devices of arbitrary size
type: journal_article
user_id: '48188'
volume: 6
year: '2024'
...
---
_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'
...