---
_id: '51204'
abstract:
- lang: eng
  text: "Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup
    $\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup
    $\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant
    differential operators, and the decay of matrix coefficients. In\r\nparticular,
    this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash
    G)$ in this general setting."
author:
- first_name: Christopher
  full_name: Lutsko, Christopher
  last_name: Lutsko
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
  full_name: Wolf, Lasse Lennart
  id: '45027'
  last_name: Wolf
  orcid: 0000-0001-8893-2045
citation:
  ama: Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness
    of locally  symmetric spaces. <i>Duke Math Journal </i>. 2026;(to appear).
  apa: Lutsko, C., Weich, T., &#38; Wolf, L. L. (2026). Polyhedral bounds on the joint
    spectrum and temperedness of locally  symmetric spaces. <i>Duke Math. Journal
    </i>, <i>(to appear)</i>.
  bibtex: '@article{Lutsko_Weich_Wolf_2026, title={Polyhedral bounds on the joint
    spectrum and temperedness of locally  symmetric spaces}, volume={(to appear)},
    journal={Duke Math. Journal }, author={Lutsko, Christopher and Weich, Tobias and
    Wolf, Lasse Lennart}, year={2026} }'
  chicago: Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral
    Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” <i>Duke
    Math. Journal </i> (to appear) (2026).
  ieee: C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum
    and temperedness of locally  symmetric spaces,” <i>Duke Math. Journal </i>, vol.
    (to appear), 2026.
  mla: Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness
    of Locally  Symmetric Spaces.” <i>Duke Math. Journal </i>, vol. (to appear), 2026.
  short: C. Lutsko, T. Weich, L.L. Wolf, Duke Math. Journal  (to appear) (2026).
date_created: 2024-02-06T20:35:36Z
date_updated: 2026-02-18T10:37:47Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
  arxiv:
  - '2402.02530'
language:
- iso: eng
publication: 'Duke Math. Journal '
status: public
title: Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric
  spaces
type: journal_article
user_id: '49178'
volume: (to appear)
year: '2026'
...
---
_id: '65255'
abstract:
- lang: eng
  text: In this paper we generalize the geodesic flow on (finite) homogeneous graphs
    to a multiparameter flow on compact quotients of Euclidean buildings. Then we
    study the joint spectra of the associated transfer operators acting on suitable
    Lipschitz spaces. The main result says that outside an arbitrarily small neighborhood
    of zero in the set of spectral parameters the Taylor spectrum of the commuting
    family of transfer operators is contained in the joint point spectrum.
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Daniel
  full_name: Kahl, Daniel
  id: '55661'
  last_name: Kahl
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Hilgert J, Kahl D, Weich T. Spectral theory for transfer operators on compact
    quotients of Euclidean buildings. <i>arXiv:260326949</i>. Published online 2026.
  apa: Hilgert, J., Kahl, D., &#38; Weich, T. (2026). Spectral theory for transfer
    operators on compact quotients of Euclidean buildings. In <i>arXiv:2603.26949</i>.
  bibtex: '@article{Hilgert_Kahl_Weich_2026, title={Spectral theory for transfer operators
    on compact quotients of Euclidean buildings}, journal={arXiv:2603.26949}, author={Hilgert,
    Joachim and Kahl, Daniel and Weich, Tobias}, year={2026} }'
  chicago: Hilgert, Joachim, Daniel Kahl, and Tobias Weich. “Spectral Theory for Transfer
    Operators on Compact Quotients of Euclidean Buildings.” <i>ArXiv:2603.26949</i>,
    2026.
  ieee: J. Hilgert, D. Kahl, and T. Weich, “Spectral theory for transfer operators
    on compact quotients of Euclidean buildings,” <i>arXiv:2603.26949</i>. 2026.
  mla: Hilgert, Joachim, et al. “Spectral Theory for Transfer Operators on Compact
    Quotients of Euclidean Buildings.” <i>ArXiv:2603.26949</i>, 2026.
  short: J. Hilgert, D. Kahl, T. Weich, ArXiv:2603.26949 (2026).
date_created: 2026-03-31T08:30:34Z
date_updated: 2026-03-31T08:31:01Z
external_id:
  arxiv:
  - '2603.26949'
language:
- iso: eng
publication: arXiv:2603.26949
status: public
title: Spectral theory for transfer operators on compact quotients of Euclidean buildings
type: preprint
user_id: '220'
year: '2026'
...
---
_id: '32099'
author:
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Julia
  full_name: Budde, Julia
  last_name: Budde
citation:
  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>
  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>
  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} }'
  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>.'
  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>.
  short: T. Weich, J. Budde, Journal of Functional Analysis 288 (2025).
date_created: 2022-06-22T09:56:43Z
date_updated: 2024-09-25T08:18:44Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: ' https://doi.org/10.1016/j.jfa.2024.110684'
file:
- access_level: open_access
  content_type: application/pdf
  creator: weich
  date_created: 2022-06-22T09:56:39Z
  date_updated: 2022-06-22T09:56:39Z
  file_id: '32100'
  file_name: 2103.02968.pdf
  file_size: 978990
  relation: main_file
file_date_updated: 2022-06-22T09:56:39Z
has_accepted_license: '1'
intvolume: '       288'
issue: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '356'
  grant_number: '491392403'
  name: 'TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem
    Volumen (Teilprojekt B02)'
- _id: '355'
  grant_number: '422642921'
  name: Mikrolokale Methoden für hyperbolische Dynamiken
publication: Journal of Functional Analysis
status: public
title: Wave Front Sets of Nilpotent Lie Group Representations
type: journal_article
user_id: '49178'
volume: 288
year: '2025'
...
---
_id: '51207'
abstract:
- lang: eng
  text: "Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact
    type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We
    show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic
    growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain
    that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$."
article_number: '76'
author:
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
  full_name: Wolf, Lasse Lennart
  id: '45027'
  last_name: Wolf
  orcid: 0000-0001-8893-2045
citation:
  ama: 'Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case.
    <i>Geom Dedicata</i>. 2024;218. doi:<a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>'
  apa: 'Weich, T., &#38; Wolf, L. L. (2024). Temperedness of locally symmetric spaces:
    The product case. <i>Geom Dedicata</i>, <i>218</i>, Article 76. <a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>'
  bibtex: '@article{Weich_Wolf_2024, title={Temperedness of locally symmetric spaces:
    The product case}, volume={218}, DOI={<a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>},
    number={76}, journal={Geom Dedicata}, author={Weich, Tobias and Wolf, Lasse Lennart},
    year={2024} }'
  chicago: 'Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric
    Spaces: The Product Case.” <i>Geom Dedicata</i> 218 (2024). <a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>.'
  ieee: 'T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product
    case,” <i>Geom Dedicata</i>, vol. 218, Art. no. 76, 2024, doi: <a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>.'
  mla: 'Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric
    Spaces: The Product Case.” <i>Geom Dedicata</i>, vol. 218, 76, 2024, doi:<a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>.'
  short: T. Weich, L.L. Wolf, Geom Dedicata 218 (2024).
date_created: 2024-02-06T21:00:55Z
date_updated: 2024-05-07T11:44:34Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: https://doi.org/10.1007/s10711-024-00904-4
external_id:
  arxiv:
  - '2304.09573'
intvolume: '       218'
language:
- iso: eng
publication: Geom Dedicata
status: public
title: 'Temperedness of locally symmetric spaces: The product case'
type: journal_article
user_id: '45027'
volume: 218
year: '2024'
...
---
_id: '55193'
author:
- first_name: Max
  full_name: Hoffmann, Max
  id: '32202'
  last_name: Hoffmann
  orcid: 0000-0002-6964-7123
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Hoffmann M, Hilgert J, Weich T. <i>Ebene euklidische Geometrie. Algebraisierung,
    Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg;
    2024. doi:<a href="https://doi.org/10.1007/978-3-662-67357-7">10.1007/978-3-662-67357-7</a>
  apa: Hoffmann, M., Hilgert, J., &#38; Weich, T. (2024). <i>Ebene euklidische Geometrie.
    Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer
    Berlin Heidelberg. <a href="https://doi.org/10.1007/978-3-662-67357-7">https://doi.org/10.1007/978-3-662-67357-7</a>
  bibtex: '@book{Hoffmann_Hilgert_Weich_2024, place={Berlin, Heidelberg}, title={Ebene
    euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur
    Schulmathematik}, DOI={<a href="https://doi.org/10.1007/978-3-662-67357-7">10.1007/978-3-662-67357-7</a>},
    publisher={Springer Berlin Heidelberg}, author={Hoffmann, Max and Hilgert, Joachim
    and Weich, Tobias}, year={2024} }'
  chicago: 'Hoffmann, Max, Joachim Hilgert, and Tobias Weich. <i>Ebene euklidische
    Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>.
    Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. <a href="https://doi.org/10.1007/978-3-662-67357-7">https://doi.org/10.1007/978-3-662-67357-7</a>.'
  ieee: 'M. Hoffmann, J. Hilgert, and T. Weich, <i>Ebene euklidische Geometrie. Algebraisierung,
    Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Berlin, Heidelberg:
    Springer Berlin Heidelberg, 2024.'
  mla: Hoffmann, Max, et al. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung
    und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg, 2024,
    doi:<a href="https://doi.org/10.1007/978-3-662-67357-7">10.1007/978-3-662-67357-7</a>.
  short: M. Hoffmann, J. Hilgert, T. Weich, Ebene euklidische Geometrie. Algebraisierung,
    Axiomatisierung und Schnittstellen zur Schulmathematik, Springer Berlin Heidelberg,
    Berlin, Heidelberg, 2024.
date_created: 2024-07-12T08:36:42Z
date_updated: 2024-08-08T08:05:30Z
department:
- _id: '97'
- _id: '643'
- _id: '548'
doi: 10.1007/978-3-662-67357-7
language:
- iso: ger
place: Berlin, Heidelberg
publication_identifier:
  isbn:
  - '9783662673560'
  - '9783662673577'
publication_status: published
publisher: Springer Berlin Heidelberg
status: public
title: Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen
  zur Schulmathematik
type: book
user_id: '220'
year: '2024'
...
---
_id: '32101'
author:
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Yannick
  full_name: Guedes Bonthonneau, Yannick
  last_name: Guedes Bonthonneau
- first_name: Colin
  full_name: Guillarmou, Colin
  last_name: Guillarmou
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonances
    of Anosov actions. <i>J Europ Math Soc</i>. 2024;27(8):3085–3147. doi:<a href="https://doi.org/10.4171/JEMS/1428">https://doi.org/10.4171/JEMS/1428</a>
  apa: Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., &#38; Hilgert, J. (2024).
    Ruelle-Taylor resonances of Anosov actions. <i>J. Europ. Math. Soc.</i>, <i>27</i>(8),
    3085–3147. <a href="https://doi.org/10.4171/JEMS/1428">https://doi.org/10.4171/JEMS/1428</a>
  bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor
    resonances of Anosov actions}, volume={27}, DOI={<a href="https://doi.org/10.4171/JEMS/1428">https://doi.org/10.4171/JEMS/1428</a>},
    number={8}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias and Guedes Bonthonneau,
    Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024}, pages={3085–3147}
    }'
  chicago: 'Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim
    Hilgert. “Ruelle-Taylor Resonances of Anosov Actions.” <i>J. Europ. Math. Soc.</i>
    27, no. 8 (2024): 3085–3147. <a href="https://doi.org/10.4171/JEMS/1428">https://doi.org/10.4171/JEMS/1428</a>.'
  ieee: 'T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor
    resonances of Anosov actions,” <i>J. Europ. Math. Soc.</i>, vol. 27, no. 8, pp.
    3085–3147, 2024, doi: <a href="https://doi.org/10.4171/JEMS/1428">https://doi.org/10.4171/JEMS/1428</a>.'
  mla: Weich, Tobias, et al. “Ruelle-Taylor Resonances of Anosov Actions.” <i>J. Europ.
    Math. Soc.</i>, vol. 27, no. 8, 2024, pp. 3085–3147, doi:<a href="https://doi.org/10.4171/JEMS/1428">https://doi.org/10.4171/JEMS/1428</a>.
  short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math.
    Soc. 27 (2024) 3085–3147.
date_created: 2022-06-22T09:56:51Z
date_updated: 2026-02-18T10:33:34Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
- _id: '91'
doi: https://doi.org/10.4171/JEMS/1428
file:
- access_level: open_access
  content_type: application/pdf
  creator: weich
  date_created: 2022-06-22T09:56:47Z
  date_updated: 2022-06-22T09:56:47Z
  file_id: '32102'
  file_name: 2007.14275.pdf
  file_size: 796410
  relation: main_file
file_date_updated: 2022-06-22T09:56:47Z
has_accepted_license: '1'
intvolume: '        27'
issue: '8'
language:
- iso: eng
oa: '1'
page: 3085–3147
publication: J. Europ. Math. Soc.
publication_status: published
status: public
title: Ruelle-Taylor resonances of Anosov actions
type: journal_article
user_id: '49178'
volume: 27
year: '2024'
...
---
_id: '32097'
author:
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Yannick
  full_name: Guedes Bonthonneau, Yannick
  last_name: Guedes Bonthonneau
- first_name: Colin
  full_name: Guillarmou, Colin
  last_name: Guillarmou
citation:
  ama: 'Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions.
    <i>Journal of Differential Geometry</i>. 2024;128:959-1026. doi:<a href="https://doi.org/
    DOI: 10.4310/jdg/1729092452"> DOI: 10.4310/jdg/1729092452</a>'
  apa: 'Weich, T., Guedes Bonthonneau, Y., &#38; Guillarmou, C. (2024). SRB Measures
    of Anosov Actions. <i>Journal of Differential Geometry</i>, <i>128</i>, 959–1026.
    <a href="https://doi.org/ DOI: 10.4310/jdg/1729092452">https://doi.org/ DOI: 10.4310/jdg/1729092452</a>'
  bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures
    of Anosov Actions}, volume={128}, DOI={<a href="https://doi.org/ DOI: 10.4310/jdg/1729092452">
    DOI: 10.4310/jdg/1729092452</a>}, journal={Journal of Differential Geometry},
    author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin},
    year={2024}, pages={959–1026} }'
  chicago: 'Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB
    Measures of Anosov Actions.” <i>Journal of Differential Geometry</i> 128 (2024):
    959–1026. <a href="https://doi.org/ DOI: 10.4310/jdg/1729092452">https://doi.org/
    DOI: 10.4310/jdg/1729092452</a>.'
  ieee: 'T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov
    Actions,” <i>Journal of Differential Geometry</i>, vol. 128, pp. 959–1026, 2024,
    doi: <a href="https://doi.org/ DOI: 10.4310/jdg/1729092452"> DOI: 10.4310/jdg/1729092452</a>.'
  mla: 'Weich, Tobias, et al. “SRB Measures of Anosov Actions.” <i>Journal of Differential
    Geometry</i>, vol. 128, 2024, pp. 959–1026, doi:<a href="https://doi.org/ DOI:
    10.4310/jdg/1729092452"> DOI: 10.4310/jdg/1729092452</a>.'
  short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry
    128 (2024) 959–1026.
date_created: 2022-06-22T09:56:23Z
date_updated: 2025-01-02T15:39:43Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: ' DOI: 10.4310/jdg/1729092452'
external_id:
  arxiv:
  - https://arxiv.org/abs/2103.12127
file:
- access_level: open_access
  content_type: application/pdf
  creator: weich
  date_created: 2022-06-22T09:56:08Z
  date_updated: 2022-06-22T09:56:08Z
  file_id: '32098'
  file_name: 2103.12127.pdf
  file_size: 745870
  relation: main_file
file_date_updated: 2022-06-22T09:56:08Z
has_accepted_license: '1'
intvolume: '       128'
language:
- iso: eng
oa: '1'
page: 959-1026
project:
- _id: '358'
  grant_number: '491392403'
  name: TRR 358 - Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden (Teilprojekt
    B04)
- _id: '355'
  grant_number: '422642921'
  name: Mikrolokale Methoden für hyperbolische Dynamiken
publication: Journal of Differential Geometry
status: public
title: SRB Measures of Anosov Actions
type: journal_article
user_id: '49178'
volume: 128
year: '2024'
...
---
_id: '58103'
author:
- first_name: K.-U.
  full_name: Bux, K.-U.
  last_name: Bux
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Bux K-U, Hilgert J, Weich T. Spectral correspondences for finite graphs without
    dead ends. <i>Indagationes Mathematicae</i>. 2024;36(1):188-217. doi:<a href="https://doi.org/10.1016/j.indag.2024.05.001">10.1016/j.indag.2024.05.001</a>
  apa: Bux, K.-U., Hilgert, J., &#38; Weich, T. (2024). Spectral correspondences for
    finite graphs without dead ends. <i>Indagationes Mathematicae</i>, <i>36</i>(1),
    188–217. <a href="https://doi.org/10.1016/j.indag.2024.05.001">https://doi.org/10.1016/j.indag.2024.05.001</a>
  bibtex: '@article{Bux_Hilgert_Weich_2024, title={Spectral correspondences for finite
    graphs without dead ends}, volume={36}, DOI={<a href="https://doi.org/10.1016/j.indag.2024.05.001">10.1016/j.indag.2024.05.001</a>},
    number={1}, journal={Indagationes Mathematicae}, publisher={Elsevier BV}, author={Bux,
    K.-U. and Hilgert, Joachim and Weich, Tobias}, year={2024}, pages={188–217} }'
  chicago: 'Bux, K.-U., Joachim Hilgert, and Tobias Weich. “Spectral Correspondences
    for Finite Graphs without Dead Ends.” <i>Indagationes Mathematicae</i> 36, no.
    1 (2024): 188–217. <a href="https://doi.org/10.1016/j.indag.2024.05.001">https://doi.org/10.1016/j.indag.2024.05.001</a>.'
  ieee: 'K.-U. Bux, J. Hilgert, and T. Weich, “Spectral correspondences for finite
    graphs without dead ends,” <i>Indagationes Mathematicae</i>, vol. 36, no. 1, pp.
    188–217, 2024, doi: <a href="https://doi.org/10.1016/j.indag.2024.05.001">10.1016/j.indag.2024.05.001</a>.'
  mla: Bux, K. U., et al. “Spectral Correspondences for Finite Graphs without Dead
    Ends.” <i>Indagationes Mathematicae</i>, vol. 36, no. 1, Elsevier BV, 2024, pp.
    188–217, doi:<a href="https://doi.org/10.1016/j.indag.2024.05.001">10.1016/j.indag.2024.05.001</a>.
  short: K.-U. Bux, J. Hilgert, T. Weich, Indagationes Mathematicae 36 (2024) 188–217.
date_created: 2025-01-08T09:39:58Z
date_updated: 2025-01-13T16:00:06Z
doi: 10.1016/j.indag.2024.05.001
intvolume: '        36'
issue: '1'
language:
- iso: eng
page: 188-217
publication: Indagationes Mathematicae
publication_identifier:
  issn:
  - 0019-3577
publication_status: published
publisher: Elsevier BV
status: public
title: Spectral correspondences for finite graphs without dead ends
type: journal_article
user_id: '220'
volume: 36
year: '2024'
...
---
_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: '31189'
abstract:
- lang: eng
  text: "Given a geometrically finite hyperbolic surface of infinite volume it is
    a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator
    has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization
    of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential
    operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of
    higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe
    geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding
    principal eigenvalues. A large class of examples fulfilling these\r\nassumptions
    are the non-compact quotients by Anosov subgroups."
author:
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
  full_name: Wolf, Lasse Lennart
  id: '45027'
  last_name: Wolf
citation:
  ama: Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally
    symmetric  spaces. <i>Communications in Mathematical Physics</i>. 2023;403. doi:<a
    href="https://doi.org/10.1007/s00220-023-04819-1">https://doi.org/10.1007/s00220-023-04819-1</a>
  apa: Weich, T., &#38; Wolf, L. L. (2023). Absence of principal eigenvalues for higher
    rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>,
    <i>403</i>. <a href="https://doi.org/10.1007/s00220-023-04819-1">https://doi.org/10.1007/s00220-023-04819-1</a>
  bibtex: '@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher
    rank locally symmetric  spaces}, volume={403}, DOI={<a href="https://doi.org/10.1007/s00220-023-04819-1">https://doi.org/10.1007/s00220-023-04819-1</a>},
    journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf,
    Lasse Lennart}, year={2023} }'
  chicago: Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues
    for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical
    Physics</i> 403 (2023). <a href="https://doi.org/10.1007/s00220-023-04819-1">https://doi.org/10.1007/s00220-023-04819-1</a>.
  ieee: 'T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank
    locally symmetric  spaces,” <i>Communications in Mathematical Physics</i>, vol.
    403, 2023, doi: <a href="https://doi.org/10.1007/s00220-023-04819-1">https://doi.org/10.1007/s00220-023-04819-1</a>.'
  mla: Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for
    Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i>,
    vol. 403, 2023, doi:<a href="https://doi.org/10.1007/s00220-023-04819-1">https://doi.org/10.1007/s00220-023-04819-1</a>.
  short: T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).
date_created: 2022-05-11T10:38:11Z
date_updated: 2024-02-06T20:52:40Z
department:
- _id: '10'
- _id: '548'
- _id: '623'
doi: https://doi.org/10.1007/s00220-023-04819-1
external_id:
  arxiv:
  - '2205.03167'
intvolume: '       403'
language:
- iso: eng
publication: Communications in Mathematical Physics
publication_identifier:
  unknown:
  - 1275-1295
status: public
title: Absence of principal eigenvalues for higher rank locally symmetric  spaces
type: journal_article
user_id: '49178'
volume: 403
year: '2023'
...
---
_id: '51206'
abstract:
- lang: eng
  text: "We present a numerical algorithm for the computation of invariant Ruelle\r\ndistributions
    on convex co-compact hyperbolic surfaces. This is achieved by\r\nexploiting the
    connection between invariant Ruelle distributions and residues\r\nof meromorphically
    continued weighted zeta functions established by the authors\r\ntogether with
    Barkhofen (2021). To make this applicable for numerics we express\r\nthe weighted
    zeta as the logarithmic derivative of a suitable parameter\r\ndependent Fredholm
    determinant similar to Borthwick (2014). As an additional\r\ndifficulty our transfer
    operator has to include a contracting direction which\r\nwe account for with techniques
    developed by Rugh (1992). We achieve a further\r\nimprovement in convergence speed
    for our algorithm in the case of surfaces with\r\nadditional symmetries by proving
    and applying a symmetry reduction of weighted\r\nzeta functions."
author:
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Schütte P, Weich T. Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic
    Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. <i>arXiv:230813463</i>.
    Published online 2023.
  apa: Schütte, P., &#38; Weich, T. (2023). Invariant Ruelle Distributions on Convex-Cocompact
    Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. In
    <i>arXiv:2308.13463</i>.
  bibtex: '@article{Schütte_Weich_2023, title={Invariant Ruelle Distributions on Convex-Cocompact
    Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions}, journal={arXiv:2308.13463},
    author={Schütte, Philipp and Weich, Tobias}, year={2023} }'
  chicago: Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on
    Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta
    Functions.” <i>ArXiv:2308.13463</i>, 2023.
  ieee: P. Schütte and T. Weich, “Invariant Ruelle Distributions on Convex-Cocompact
    Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions,” <i>arXiv:2308.13463</i>.
    2023.
  mla: Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact
    Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>,
    2023.
  short: P. Schütte, T. Weich, ArXiv:2308.13463 (2023).
date_created: 2024-02-06T20:58:35Z
date_updated: 2024-02-11T19:56:01Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
  arxiv:
  - '2308.13463'
language:
- iso: eng
publication: arXiv:2308.13463
status: public
title: Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  --
  A Numerical Algorithm via Weighted Zeta Functions
type: preprint
user_id: '49178'
year: '2023'
...
---
_id: '53410'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We consider a geodesic billiard system
    consisting of a complete Riemannian manifold and an obstacle submanifold with
    boundary at which the trajectories of the geodesic flow experience specular reflections.
    We show that if the geodesic billiard system is hyperbolic on its trapped set
    and the latter is compact and non-grazing, the techniques for open hyperbolic
    systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146,
    2016) can be applied to a smooth model for the discontinuous flow defined by the
    non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent
    for the generator of the billiard flow. As an application we prove a meromorphic
    continuation of weighted zeta functions together with explicit residue formulae.
    In particular, our results apply to scattering by convex obstacles in the Euclidean
    plane.</jats:p>
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle
    Scattering via Smooth Models. <i>Annales Henri Poincaré</i>. 2023;25(2):1607-1656.
    doi:<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>
  apa: Delarue, B., Schütte, P., &#38; Weich, T. (2023). Resonances and Weighted Zeta
    Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>,
    <i>25</i>(2), 1607–1656. <a href="https://doi.org/10.1007/s00023-023-01379-x">https://doi.org/10.1007/s00023-023-01379-x</a>
  bibtex: '@article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta
    Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>},
    number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and
    Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich,
    Tobias}, year={2023}, pages={1607–1656} }'
  chicago: 'Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and
    Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales
    Henri Poincaré</i> 25, no. 2 (2023): 1607–56. <a href="https://doi.org/10.1007/s00023-023-01379-x">https://doi.org/10.1007/s00023-023-01379-x</a>.'
  ieee: 'B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions
    for Obstacle Scattering via Smooth Models,” <i>Annales Henri Poincaré</i>, vol.
    25, no. 2, pp. 1607–1656, 2023, doi: <a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>.'
  mla: Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle
    Scattering via Smooth Models.” <i>Annales Henri Poincaré</i>, vol. 25, no. 2,
    Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>.
  short: B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.
date_created: 2024-04-11T12:30:14Z
date_updated: 2024-04-11T12:37:34Z
department:
- _id: '548'
doi: 10.1007/s00023-023-01379-x
intvolume: '        25'
issue: '2'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 1607-1656
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models
type: journal_article
user_id: '70575'
volume: 25
year: '2023'
...
---
_id: '31190'
abstract:
- lang: eng
  text: "For a compact Riemannian locally symmetric space $\\Gamma\\backslash G/K$
    of\r\narbitrary rank we determine the location of certain Ruelle-Taylor resonances\r\nfor
    the Weyl chamber action. We provide a Weyl-lower bound on an appropriate\r\ncounting
    function for the Ruelle-Taylor resonances and establish a spectral gap\r\nwhich
    is uniform in $\\Gamma$ if $G/K$ is irreducible of higher rank. This is\r\nachieved
    by proving a quantum-classical correspondence, i.e. a\r\n1:1-correspondence between
    horocyclically invariant Ruelle-Taylor resonant\r\nstates and joint eigenfunctions
    of the algebra of invariant differential\r\noperators on $G/K$."
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
  full_name: Wolf, Lasse Lennart
  id: '45027'
  last_name: Wolf
  orcid: 0000-0001-8893-2045
citation:
  ama: Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence.
    <i>Analysis &#38; PDE</i>. 2023;16(10):2241–2265. doi:<a href="https://doi.org/10.2140/apde.2023.16.2241">https://doi.org/10.2140/apde.2023.16.2241</a>
  apa: Hilgert, J., Weich, T., &#38; Wolf, L. L. (2023). Higher rank quantum-classical
    correspondence. <i>Analysis &#38; PDE</i>, <i>16</i>(10), 2241–2265. <a href="https://doi.org/10.2140/apde.2023.16.2241">https://doi.org/10.2140/apde.2023.16.2241</a>
  bibtex: '@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical
    correspondence}, volume={16}, DOI={<a href="https://doi.org/10.2140/apde.2023.16.2241">https://doi.org/10.2140/apde.2023.16.2241</a>},
    number={10}, journal={Analysis &#38; PDE}, publisher={MSP}, author={Hilgert, Joachim
    and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }'
  chicago: 'Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical
    Correspondence.” <i>Analysis &#38; PDE</i> 16, no. 10 (2023): 2241–2265. <a href="https://doi.org/10.2140/apde.2023.16.2241">https://doi.org/10.2140/apde.2023.16.2241</a>.'
  ieee: 'J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,”
    <i>Analysis &#38; PDE</i>, vol. 16, no. 10, pp. 2241–2265, 2023, doi: <a href="https://doi.org/10.2140/apde.2023.16.2241">https://doi.org/10.2140/apde.2023.16.2241</a>.'
  mla: Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” <i>Analysis
    &#38; PDE</i>, vol. 16, no. 10, MSP, 2023, pp. 2241–2265, doi:<a href="https://doi.org/10.2140/apde.2023.16.2241">https://doi.org/10.2140/apde.2023.16.2241</a>.
  short: J. Hilgert, T. Weich, L.L. Wolf, Analysis &#38; PDE 16 (2023) 2241–2265.
date_created: 2022-05-11T10:41:35Z
date_updated: 2026-02-18T10:39:36Z
department:
- _id: '10'
- _id: '548'
- _id: '91'
doi: https://doi.org/10.2140/apde.2023.16.2241
external_id:
  arxiv:
  - '2103.05667'
intvolume: '        16'
issue: '10'
language:
- iso: eng
page: 2241–2265
publication: Analysis & PDE
publisher: MSP
status: public
title: Higher rank quantum-classical correspondence
type: journal_article
user_id: '49178'
volume: 16
year: '2023'
...
---
_id: '31059'
abstract:
- lang: eng
  text: In this article we prove meromorphic continuation of weighted zeta functions
    in the framework of open hyperbolic systems by using the meromorphically continued
    restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula
    proving equality between residues of weighted zetas and invariant Ruelle distributions.
    We combine this equality with results of Guillarmou, Hilgert and Weich (2021)
    in order to relate the residues to Patterson-Sullivan distributions. Finally we
    provide proof-of-principle results concerning the numerical calculation of invariant
    Ruelle distributions for 3-disc scattering systems.
author:
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Sonja
  full_name: Barkhofen, Sonja
  id: '48188'
  last_name: Barkhofen
citation:
  ama: Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta
    Functions on Open Hyperbolic Systems. <i>Communications in Mathematical Physics</i>.
    2023;398:655-678. doi:<a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>
  apa: Schütte, P., Weich, T., &#38; Barkhofen, S. (2023). Meromorphic Continuation
    of Weighted Zeta Functions on Open Hyperbolic Systems. <i>Communications in Mathematical
    Physics</i>, <i>398</i>, 655–678. <a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>
  bibtex: '@article{Schütte_Weich_Barkhofen_2023, title={Meromorphic Continuation
    of Weighted Zeta Functions on Open Hyperbolic Systems}, volume={398}, DOI={<a
    href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>},
    journal={Communications in Mathematical Physics}, author={Schütte, Philipp and
    Weich, Tobias and Barkhofen, Sonja}, year={2023}, pages={655–678} }'
  chicago: 'Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation
    of Weighted Zeta Functions on Open Hyperbolic Systems.” <i>Communications in Mathematical
    Physics</i> 398 (2023): 655–78. <a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>.'
  ieee: 'P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted
    Zeta Functions on Open Hyperbolic Systems,” <i>Communications in Mathematical
    Physics</i>, vol. 398, pp. 655–678, 2023, doi: <a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>.'
  mla: Schütte, Philipp, et al. “Meromorphic Continuation of Weighted Zeta Functions
    on Open Hyperbolic Systems.” <i>Communications in Mathematical Physics</i>, vol.
    398, 2023, pp. 655–78, doi:<a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>.
  short: P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics
    398 (2023) 655–678.
date_created: 2022-05-04T12:27:46Z
date_updated: 2026-02-18T10:41:07Z
department:
- _id: '10'
- _id: '548'
- _id: '623'
- _id: '15'
doi: https://doi.org/10.1007/s00220-022-04538-z
external_id:
  arxiv:
  - '2112.05791'
intvolume: '       398'
language:
- iso: eng
page: 655-678
publication: Communications in Mathematical Physics
status: public
title: Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems
type: journal_article
user_id: '49178'
volume: 398
year: '2023'
...
---
_id: '35306'
author:
- first_name: Yannick
  full_name: Guedes Bonthonneau, Yannick
  last_name: Guedes Bonthonneau
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Guedes Bonthonneau Y, Weich T. Ruelle–Pollicott resonances for manifolds with
    hyperbolic cusps. <i>Journal of the European Mathematical Society</i>. 2022;24(3):851-923.
    doi:<a href="https://doi.org/10.4171/jems/1103">10.4171/jems/1103</a>
  apa: Guedes Bonthonneau, Y., &#38; Weich, T. (2022). Ruelle–Pollicott resonances
    for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>,
    <i>24</i>(3), 851–923. <a href="https://doi.org/10.4171/jems/1103">https://doi.org/10.4171/jems/1103</a>
  bibtex: '@article{Guedes Bonthonneau_Weich_2022, title={Ruelle–Pollicott resonances
    for manifolds with hyperbolic cusps}, volume={24}, DOI={<a href="https://doi.org/10.4171/jems/1103">10.4171/jems/1103</a>},
    number={3}, journal={Journal of the European Mathematical Society}, publisher={European
    Mathematical Society - EMS - Publishing House GmbH}, author={Guedes Bonthonneau,
    Yannick and Weich, Tobias}, year={2022}, pages={851–923} }'
  chicago: 'Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances
    for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical
    Society</i> 24, no. 3 (2022): 851–923. <a href="https://doi.org/10.4171/jems/1103">https://doi.org/10.4171/jems/1103</a>.'
  ieee: 'Y. Guedes Bonthonneau and T. Weich, “Ruelle–Pollicott resonances for manifolds
    with hyperbolic cusps,” <i>Journal of the European Mathematical Society</i>, vol.
    24, no. 3, pp. 851–923, 2022, doi: <a href="https://doi.org/10.4171/jems/1103">10.4171/jems/1103</a>.'
  mla: Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances
    for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical
    Society</i>, vol. 24, no. 3, European Mathematical Society - EMS - Publishing
    House GmbH, 2022, pp. 851–923, doi:<a href="https://doi.org/10.4171/jems/1103">10.4171/jems/1103</a>.
  short: Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society
    24 (2022) 851–923.
date_created: 2023-01-05T16:23:34Z
date_updated: 2023-01-06T08:47:35Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: 10.4171/jems/1103
intvolume: '        24'
issue: '3'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 851-923
publication: Journal of the European Mathematical Society
publication_identifier:
  issn:
  - 1435-9855
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
status: public
title: Ruelle–Pollicott resonances for manifolds with hyperbolic cusps
type: journal_article
user_id: '49178'
volume: 24
year: '2022'
...
---
_id: '31057'
abstract:
- lang: eng
  text: In this paper we give an overview over some aspects of the modern mathematical
    theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical
    systems and their implications in physics. First we recall recent developments
    in the mathematical theory of resonances, in particular how invariant Ruelle distributions
    arise as residues of weighted zeta functions. Then we derive a correspondence
    between weighted and semiclassical zeta functions in the setting of negatively
    curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich
    yields a high frequency interpretation of invariant Ruelle distributions as quantum
    mechanical matrix coefficients in constant negative curvature. We finish by presenting
    numerical calculations of phase space distributions in the more physical setting
    of 3-disk scattering systems.
article_number: '244007'
article_type: review
author:
- first_name: Sonja
  full_name: Barkhofen, Sonja
  id: '48188'
  last_name: Barkhofen
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: 'Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions.
    <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(24). doi:<a
    href="https://doi.org/10.1088/1751-8121/ac6d2b">10.1088/1751-8121/ac6d2b</a>'
  apa: 'Barkhofen, S., Schütte, P., &#38; Weich, T. (2022). Semiclassical formulae
    For Wigner distributions. <i>Journal of Physics A: Mathematical and Theoretical</i>,
    <i>55</i>(24), Article 244007. <a href="https://doi.org/10.1088/1751-8121/ac6d2b">https://doi.org/10.1088/1751-8121/ac6d2b</a>'
  bibtex: '@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For
    Wigner distributions}, volume={55}, DOI={<a href="https://doi.org/10.1088/1751-8121/ac6d2b">10.1088/1751-8121/ac6d2b</a>},
    number={24244007}, journal={Journal of Physics A: Mathematical and Theoretical},
    publisher={IOP Publishing Ltd}, author={Barkhofen, Sonja and Schütte, Philipp
    and Weich, Tobias}, year={2022} }'
  chicago: 'Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae
    For Wigner Distributions.” <i>Journal of Physics A: Mathematical and Theoretical</i>
    55, no. 24 (2022). <a href="https://doi.org/10.1088/1751-8121/ac6d2b">https://doi.org/10.1088/1751-8121/ac6d2b</a>.'
  ieee: 'S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner
    distributions,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol.
    55, no. 24, Art. no. 244007, 2022, doi: <a href="https://doi.org/10.1088/1751-8121/ac6d2b">10.1088/1751-8121/ac6d2b</a>.'
  mla: 'Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.”
    <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 24, 244007,
    IOP Publishing Ltd, 2022, doi:<a href="https://doi.org/10.1088/1751-8121/ac6d2b">10.1088/1751-8121/ac6d2b</a>.'
  short: 'S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and
    Theoretical 55 (2022).'
date_created: 2022-05-04T12:23:11Z
date_updated: 2024-02-06T20:40:45Z
department:
- _id: '623'
- _id: '548'
- _id: '10'
doi: 10.1088/1751-8121/ac6d2b
external_id:
  arxiv:
  - '2201.04892'
intvolume: '        55'
issue: '24'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publisher: IOP Publishing Ltd
status: public
title: Semiclassical formulae For Wigner distributions
type: journal_article
user_id: '49178'
volume: 55
year: '2022'
...
---
_id: '35322'
author:
- first_name: Kai-Uwe
  full_name: Bux, Kai-Uwe
  last_name: Bux
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree.
    <i>Journal of Spectral Theory</i>. 2022;12(2):659-681. doi:<a href="https://doi.org/10.4171/jst/414">10.4171/jst/414</a>
  apa: Bux, K.-U., Hilgert, J., &#38; Weich, T. (2022). Poisson transforms for trees
    of bounded degree. <i>Journal of Spectral Theory</i>, <i>12</i>(2), 659–681. <a
    href="https://doi.org/10.4171/jst/414">https://doi.org/10.4171/jst/414</a>
  bibtex: '@article{Bux_Hilgert_Weich_2022, title={Poisson transforms for trees of
    bounded degree}, volume={12}, DOI={<a href="https://doi.org/10.4171/jst/414">10.4171/jst/414</a>},
    number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical
    Society - EMS - Publishing House GmbH}, author={Bux, Kai-Uwe and Hilgert, Joachim
    and Weich, Tobias}, year={2022}, pages={659–681} }'
  chicago: 'Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Poisson Transforms for
    Trees of Bounded Degree.” <i>Journal of Spectral Theory</i> 12, no. 2 (2022):
    659–81. <a href="https://doi.org/10.4171/jst/414">https://doi.org/10.4171/jst/414</a>.'
  ieee: 'K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded
    degree,” <i>Journal of Spectral Theory</i>, vol. 12, no. 2, pp. 659–681, 2022,
    doi: <a href="https://doi.org/10.4171/jst/414">10.4171/jst/414</a>.'
  mla: Bux, Kai-Uwe, et al. “Poisson Transforms for Trees of Bounded Degree.” <i>Journal
    of Spectral Theory</i>, vol. 12, no. 2, European Mathematical Society - EMS -
    Publishing House GmbH, 2022, pp. 659–81, doi:<a href="https://doi.org/10.4171/jst/414">10.4171/jst/414</a>.
  short: K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.
date_created: 2023-01-06T08:49:06Z
date_updated: 2024-02-19T06:28:12Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
- _id: '91'
doi: 10.4171/jst/414
intvolume: '        12'
issue: '2'
keyword:
- Geometry and Topology
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 659-681
publication: Journal of Spectral Theory
publication_identifier:
  issn:
  - 1664-039X
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
status: public
title: Poisson transforms for trees of bounded degree
type: journal_article
user_id: '49063'
volume: 12
year: '2022'
...
---
_id: '51385'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: K.-U.
  full_name: Bux, K.-U.
  last_name: Bux
citation:
  ama: Hilgert J, Weich T, Bux K-U. Poisson transforms for trees of bounded degree.
    <i>J of Spectral Theory</i>. 2022;12:659-681.
  apa: Hilgert, J., Weich, T., &#38; Bux, K.-U. (2022). Poisson transforms for trees
    of bounded degree. <i>J. of Spectral Theory</i>, <i>12</i>, 659–681.
  bibtex: '@article{Hilgert_Weich_Bux_2022, title={Poisson transforms for trees of
    bounded degree}, volume={12}, journal={J. of Spectral Theory}, author={Hilgert,
    Joachim and Weich, Tobias and Bux, K.-U.}, year={2022}, pages={659–681} }'
  chicago: 'Hilgert, Joachim, Tobias Weich, and K.-U. Bux. “Poisson Transforms for
    Trees of Bounded Degree.” <i>J. of Spectral Theory</i> 12 (2022): 659–81.'
  ieee: J. Hilgert, T. Weich, and K.-U. Bux, “Poisson transforms for trees of bounded
    degree,” <i>J. of Spectral Theory</i>, vol. 12, pp. 659–681, 2022.
  mla: Hilgert, Joachim, et al. “Poisson Transforms for Trees of Bounded Degree.”
    <i>J. of Spectral Theory</i>, vol. 12, 2022, pp. 659–81.
  short: J. Hilgert, T. Weich, K.-U. Bux, J. of Spectral Theory 12 (2022) 659–681.
date_created: 2024-02-19T06:36:17Z
date_updated: 2026-03-31T08:25:35Z
department:
- _id: '91'
intvolume: '        12'
language:
- iso: eng
page: 659-681
publication: J. of Spectral Theory
publication_status: published
status: public
title: Poisson transforms for trees of bounded degree
type: journal_article
user_id: '220'
volume: 12
year: '2022'
...
---
_id: '31058'
abstract:
- lang: eng
  text: We consider a geodesic billiard system consisting of a complete Riemannian
    manifold and an obstacle submanifold with boundary at which the trajectories of
    the geodesic flow experience specular reflections. We show that if the geodesic
    billiard system is hyperbolic on its trapped set and the latter is compact and
    non-grazing the techniques for open hyperbolic systems developed by Dyatlov and
    Guillarmou can be applied to a smooth model for the discontinuous flow defined
    by the non-grazing billiard trajectories. This allows us to obtain a meromorphic
    resolvent for the generator of the billiard flow. As an application we prove a
    meromorphic continuation of weighted zeta functions together with explicit residue
    formulae. In particular, our results apply to scattering by convex obstacles in
    the Euclidean plane.
author:
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Benjamin
  full_name: Delarue, Benjamin
  last_name: Delarue
citation:
  ama: Schütte P, Weich T, Delarue B. Resonances and weighted zeta functions for obstacle
    scattering via smooth models. Published online 2021.
  apa: Schütte, P., Weich, T., &#38; Delarue, B. (2021). <i>Resonances and weighted
    zeta functions for obstacle scattering via smooth models</i>.
  bibtex: '@article{Schütte_Weich_Delarue_2021, title={Resonances and weighted zeta
    functions for obstacle scattering via smooth models}, author={Schütte, Philipp
    and Weich, Tobias and Delarue, Benjamin}, year={2021} }'
  chicago: Schütte, Philipp, Tobias Weich, and Benjamin Delarue. “Resonances and Weighted
    Zeta Functions for Obstacle Scattering via Smooth Models,” 2021.
  ieee: P. Schütte, T. Weich, and B. Delarue, “Resonances and weighted zeta functions
    for obstacle scattering via smooth models.” 2021.
  mla: Schütte, Philipp, et al. <i>Resonances and Weighted Zeta Functions for Obstacle
    Scattering via Smooth Models</i>. 2021.
  short: P. Schütte, T. Weich, B. Delarue, (2021).
date_created: 2022-05-04T12:25:58Z
date_updated: 2022-05-17T12:05:52Z
department:
- _id: '10'
- _id: '548'
external_id:
  arxiv:
  - '2109.05907'
language:
- iso: eng
status: public
title: Resonances and weighted zeta functions for obstacle scattering via smooth models
type: preprint
user_id: '50168'
year: '2021'
...
---
_id: '31263'
author:
- first_name: Colin
  full_name: Guillarmou, Colin
  last_name: Guillarmou
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Guillarmou C, Hilgert J, Weich T. High frequency limits for invariant Ruelle
    densities. <i>Annales Henri Lebesgue</i>. 2021;4:81-119. doi:<a href="https://doi.org/10.5802/ahl.67">10.5802/ahl.67</a>
  apa: Guillarmou, C., Hilgert, J., &#38; Weich, T. (2021). High frequency limits
    for invariant Ruelle densities. <i>Annales Henri Lebesgue</i>, <i>4</i>, 81–119.
    <a href="https://doi.org/10.5802/ahl.67">https://doi.org/10.5802/ahl.67</a>
  bibtex: '@article{Guillarmou_Hilgert_Weich_2021, title={High frequency limits for
    invariant Ruelle densities}, volume={4}, DOI={<a href="https://doi.org/10.5802/ahl.67">10.5802/ahl.67</a>},
    journal={Annales Henri Lebesgue}, publisher={Cellule MathDoc/CEDRAM}, author={Guillarmou,
    Colin and Hilgert, Joachim and Weich, Tobias}, year={2021}, pages={81–119} }'
  chicago: 'Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “High Frequency
    Limits for Invariant Ruelle Densities.” <i>Annales Henri Lebesgue</i> 4 (2021):
    81–119. <a href="https://doi.org/10.5802/ahl.67">https://doi.org/10.5802/ahl.67</a>.'
  ieee: 'C. Guillarmou, J. Hilgert, and T. Weich, “High frequency limits for invariant
    Ruelle densities,” <i>Annales Henri Lebesgue</i>, vol. 4, pp. 81–119, 2021, doi:
    <a href="https://doi.org/10.5802/ahl.67">10.5802/ahl.67</a>.'
  mla: Guillarmou, Colin, et al. “High Frequency Limits for Invariant Ruelle Densities.”
    <i>Annales Henri Lebesgue</i>, vol. 4, Cellule MathDoc/CEDRAM, 2021, pp. 81–119,
    doi:<a href="https://doi.org/10.5802/ahl.67">10.5802/ahl.67</a>.
  short: C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119.
date_created: 2022-05-17T12:05:17Z
date_updated: 2024-02-19T06:27:43Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
- _id: '91'
doi: 10.5802/ahl.67
external_id:
  arxiv:
  - '1803.06717'
intvolume: '         4'
language:
- iso: eng
page: 81-119
publication: Annales Henri Lebesgue
publication_identifier:
  issn:
  - 2644-9463
publication_status: published
publisher: Cellule MathDoc/CEDRAM
status: public
title: High frequency limits for invariant Ruelle densities
type: journal_article
user_id: '49063'
volume: 4
year: '2021'
...