---
_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: '58402'
article_number: '21'
author:
- first_name: Thomas
  full_name: Baier, Thomas
  last_name: Baier
- first_name: Ana Cristina
  full_name: Ferreira, Ana Cristina
  last_name: Ferreira
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: José M.
  full_name: Mourão, José M.
  last_name: Mourão
- first_name: João P.
  full_name: Nunes, João P.
  last_name: Nunes
citation:
  ama: Baier T, Ferreira AC, Hilgert J, Mourão JM, Nunes JP. Fibering polarizations
    and Mabuchi rays on symmetric spaces of compact type. <i>Analysis and Mathematical
    Physics</i>. 2025;15(1). doi:<a href="https://doi.org/10.1007/s13324-025-01012-6">10.1007/s13324-025-01012-6</a>
  apa: Baier, T., Ferreira, A. C., Hilgert, J., Mourão, J. M., &#38; Nunes, J. P.
    (2025). Fibering polarizations and Mabuchi rays on symmetric spaces of compact
    type. <i>Analysis and Mathematical Physics</i>, <i>15</i>(1), Article 21. <a href="https://doi.org/10.1007/s13324-025-01012-6">https://doi.org/10.1007/s13324-025-01012-6</a>
  bibtex: '@article{Baier_Ferreira_Hilgert_Mourão_Nunes_2025, title={Fibering polarizations
    and Mabuchi rays on symmetric spaces of compact type}, volume={15}, DOI={<a href="https://doi.org/10.1007/s13324-025-01012-6">10.1007/s13324-025-01012-6</a>},
    number={121}, journal={Analysis and Mathematical Physics}, publisher={Springer
    Science and Business Media LLC}, author={Baier, Thomas and Ferreira, Ana Cristina
    and Hilgert, Joachim and Mourão, José M. and Nunes, João P.}, year={2025} }'
  chicago: Baier, Thomas, Ana Cristina Ferreira, Joachim Hilgert, José M. Mourão,
    and João P. Nunes. “Fibering Polarizations and Mabuchi Rays on Symmetric Spaces
    of Compact Type.” <i>Analysis and Mathematical Physics</i> 15, no. 1 (2025). <a
    href="https://doi.org/10.1007/s13324-025-01012-6">https://doi.org/10.1007/s13324-025-01012-6</a>.
  ieee: 'T. Baier, A. C. Ferreira, J. Hilgert, J. M. Mourão, and J. P. Nunes, “Fibering
    polarizations and Mabuchi rays on symmetric spaces of compact type,” <i>Analysis
    and Mathematical Physics</i>, vol. 15, no. 1, Art. no. 21, 2025, doi: <a href="https://doi.org/10.1007/s13324-025-01012-6">10.1007/s13324-025-01012-6</a>.'
  mla: Baier, Thomas, et al. “Fibering Polarizations and Mabuchi Rays on Symmetric
    Spaces of Compact Type.” <i>Analysis and Mathematical Physics</i>, vol. 15, no.
    1, 21, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s13324-025-01012-6">10.1007/s13324-025-01012-6</a>.
  short: T. Baier, A.C. Ferreira, J. Hilgert, J.M. Mourão, J.P. Nunes, Analysis and
    Mathematical Physics 15 (2025).
date_created: 2025-01-30T07:45:52Z
date_updated: 2025-01-30T07:46:30Z
doi: 10.1007/s13324-025-01012-6
intvolume: '        15'
issue: '1'
language:
- iso: eng
publication: Analysis and Mathematical Physics
publication_identifier:
  issn:
  - 1664-2368
  - 1664-235X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Fibering polarizations and Mabuchi rays on symmetric spaces of compact type
type: journal_article
user_id: '220'
volume: 15
year: '2025'
...
---
_id: '59344'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>For a finite graph,
    we establish natural isomorphisms between eigenspaces of a Laplace operator acting
    on functions on the edges and eigenspaces of a transfer operator acting on functions
    on one-sided infinite non-backtracking paths. Interpreting the transfer operator
    as a classical dynamical system and the Laplace operator as its quantization,
    this result can be viewed as a <jats:italic>quantum-classical correspondence</jats:italic>.
    In contrast to previously established quantum-classical correspondences for the
    vertex Laplacian which exclude certain exceptional spectral parameters, our correspondence
    is valid for all parameters. This allows us to relate certain spectral quantities
    to topological properties of the graph such as the cyclomatic number and the 2-colorability.
    The quantum-classical correspondence for the edge Laplacian is induced by an edge
    Poisson transform on the universal covering of the graph which is a tree of bounded
    degree. In the special case of regular trees, we relate both the vertex and the
    edge Poisson transform to the representation theory of the automorphism group
    of the tree and study associated operator valued Hecke algebras.</jats:p>"
author:
- first_name: Christian
  full_name: Arends, Christian
  last_name: Arends
- first_name: Jan
  full_name: Frahm, Jan
  last_name: Frahm
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Arends C, Frahm J, Hilgert J. Edge Laplacians and Edge Poisson Transforms for
    Graphs. <i>Potential Analysis</i>. Published online 2025. doi:<a href="https://doi.org/10.1007/s11118-024-10184-y">10.1007/s11118-024-10184-y</a>
  apa: Arends, C., Frahm, J., &#38; Hilgert, J. (2025). Edge Laplacians and Edge Poisson
    Transforms for Graphs. <i>Potential Analysis</i>. <a href="https://doi.org/10.1007/s11118-024-10184-y">https://doi.org/10.1007/s11118-024-10184-y</a>
  bibtex: '@article{Arends_Frahm_Hilgert_2025, title={Edge Laplacians and Edge Poisson
    Transforms for Graphs}, DOI={<a href="https://doi.org/10.1007/s11118-024-10184-y">10.1007/s11118-024-10184-y</a>},
    journal={Potential Analysis}, publisher={Springer Science and Business Media LLC},
    author={Arends, Christian and Frahm, Jan and Hilgert, Joachim}, year={2025} }'
  chicago: Arends, Christian, Jan Frahm, and Joachim Hilgert. “Edge Laplacians and
    Edge Poisson Transforms for Graphs.” <i>Potential Analysis</i>, 2025. <a href="https://doi.org/10.1007/s11118-024-10184-y">https://doi.org/10.1007/s11118-024-10184-y</a>.
  ieee: 'C. Arends, J. Frahm, and J. Hilgert, “Edge Laplacians and Edge Poisson Transforms
    for Graphs,” <i>Potential Analysis</i>, 2025, doi: <a href="https://doi.org/10.1007/s11118-024-10184-y">10.1007/s11118-024-10184-y</a>.'
  mla: Arends, Christian, et al. “Edge Laplacians and Edge Poisson Transforms for
    Graphs.” <i>Potential Analysis</i>, Springer Science and Business Media LLC, 2025,
    doi:<a href="https://doi.org/10.1007/s11118-024-10184-y">10.1007/s11118-024-10184-y</a>.
  short: C. Arends, J. Frahm, J. Hilgert, Potential Analysis (2025).
date_created: 2025-04-04T08:02:14Z
date_updated: 2025-04-04T08:02:34Z
doi: 10.1007/s11118-024-10184-y
language:
- iso: eng
publication: Potential Analysis
publication_identifier:
  issn:
  - 0926-2601
  - 1572-929X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Edge Laplacians and Edge Poisson Transforms for Graphs
type: journal_article
user_id: '220'
year: '2025'
...
---
_id: '59343'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>On a finite regular
    graph, (co)resonant states are eigendistributions of the transfer operator associated
    to the shift on one-sided infinite non-backtracking paths. We introduce two pairings
    of resonant and coresonant states, the <jats:italic>vertex pairing</jats:italic>
    which involves only the dependence on the initial/terminal vertex of the path,
    and the <jats:italic>geodesic pairing</jats:italic> which is given by integrating
    over all geodesics the evaluation of the coresonant state on the first half of
    the geodesic times the resonant state on the second half. The main result is that
    these two pairings coincide up to a constant which depends on the resonance, i.e.
    the corresponding eigenvalue of the transfer operator.</jats:p>"
author:
- first_name: Christian
  full_name: Arends, Christian
  last_name: Arends
- first_name: Jan
  full_name: Frahm, Jan
  last_name: Frahm
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Arends C, Frahm J, Hilgert J. A pairing formula for resonant states on finite
    regular graphs. <i>Mathematische Annalen</i>. Published online 2025. doi:<a href="https://doi.org/10.1007/s00208-025-03140-7">10.1007/s00208-025-03140-7</a>
  apa: Arends, C., Frahm, J., &#38; Hilgert, J. (2025). A pairing formula for resonant
    states on finite regular graphs. <i>Mathematische Annalen</i>. <a href="https://doi.org/10.1007/s00208-025-03140-7">https://doi.org/10.1007/s00208-025-03140-7</a>
  bibtex: '@article{Arends_Frahm_Hilgert_2025, title={A pairing formula for resonant
    states on finite regular graphs}, DOI={<a href="https://doi.org/10.1007/s00208-025-03140-7">10.1007/s00208-025-03140-7</a>},
    journal={Mathematische Annalen}, publisher={Springer Science and Business Media
    LLC}, author={Arends, Christian and Frahm, Jan and Hilgert, Joachim}, year={2025}
    }'
  chicago: Arends, Christian, Jan Frahm, and Joachim Hilgert. “A Pairing Formula for
    Resonant States on Finite Regular Graphs.” <i>Mathematische Annalen</i>, 2025.
    <a href="https://doi.org/10.1007/s00208-025-03140-7">https://doi.org/10.1007/s00208-025-03140-7</a>.
  ieee: 'C. Arends, J. Frahm, and J. Hilgert, “A pairing formula for resonant states
    on finite regular graphs,” <i>Mathematische Annalen</i>, 2025, doi: <a href="https://doi.org/10.1007/s00208-025-03140-7">10.1007/s00208-025-03140-7</a>.'
  mla: Arends, Christian, et al. “A Pairing Formula for Resonant States on Finite
    Regular Graphs.” <i>Mathematische Annalen</i>, Springer Science and Business Media
    LLC, 2025, doi:<a href="https://doi.org/10.1007/s00208-025-03140-7">10.1007/s00208-025-03140-7</a>.
  short: C. Arends, J. Frahm, J. Hilgert, Mathematische Annalen (2025).
date_created: 2025-04-04T07:59:29Z
date_updated: 2025-04-04T07:59:58Z
doi: 10.1007/s00208-025-03140-7
language:
- iso: eng
publication: Mathematische Annalen
publication_identifier:
  issn:
  - 0025-5831
  - 1432-1807
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A pairing formula for resonant states on finite regular graphs
type: journal_article
user_id: '220'
year: '2025'
...
---
_id: '64736'
citation:
  ama: Frahm J, Glöckner H, Hilgert J, Olafsson G, eds. <i>Special Issue of Journal
    of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday</i>.
    Vol 35.; 2025.
  apa: Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the
    occasion of his 60th birthday. (2025). In J. Frahm, H. Glöckner, J. Hilgert, &#38;
    G. Olafsson (Eds.), <i>J. Lie Theory</i> (Vol. 35, Issue 4).
  bibtex: '@book{Frahm_Glöckner_Hilgert_Olafsson_2025, title={Special issue of Journal
    of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday},
    volume={35}, number={4}, journal={J. Lie Theory}, year={2025} }'
  chicago: Frahm, Jan, Helge Glöckner, Joachim Hilgert, and Gestur Olafsson, eds.
    <i>Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the
    Occasion of His 60th Birthday</i>. <i>J. Lie Theory</i>. Vol. 35, 2025.
  ieee: J. Frahm, H. Glöckner, J. Hilgert, and G. Olafsson, Eds., <i>Special issue
    of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his
    60th birthday</i>, vol. 35, no. 4. 2025.
  mla: Frahm, Jan, et al., editors. “Special Issue of Journal of Lie Theory Dedicated
    to Karl-Hermann Neeb on the Occasion of His 60th Birthday.” <i>J. Lie Theory</i>,
    vol. 35, no. 4, 2025.
  short: J. Frahm, H. Glöckner, J. Hilgert, G. Olafsson, eds., Special Issue of Journal
    of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday,
    2025.
date_created: 2026-02-26T17:42:01Z
date_updated: 2026-02-26T17:51:43Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
editor:
- first_name: Jan
  full_name: Frahm, Jan
  last_name: Frahm
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Gestur
  full_name: Olafsson, Gestur
  last_name: Olafsson
intvolume: '        35'
issue: '4'
language:
- iso: eng
publication: J. Lie Theory
quality_controlled: '1'
status: public
title: Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the
  occasion of his 60th birthday
type: journal_editor
user_id: '178'
volume: 35
year: '2025'
...
---
_id: '58587'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: 'Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces.
    In: <i>Symmetry in Geometry and Analysis, Volume 2</i>. ; 2025. doi:<a href="https://doi.org/10.1007/978-981-97-7662-7">https://doi.org/10.1007/978-981-97-7662-7</a>'
  apa: Hilgert, J. (2025). Quantum-Classical Correspondences for Locally Symmetric
    Spaces. In <i>Symmetry in Geometry and Analysis, Volume 2</i>. <a href="https://doi.org/10.1007/978-981-97-7662-7">https://doi.org/10.1007/978-981-97-7662-7</a>
  bibtex: '@inbook{Hilgert_2025, title={Quantum-Classical Correspondences for Locally
    Symmetric Spaces}, DOI={<a href="https://doi.org/10.1007/978-981-97-7662-7">https://doi.org/10.1007/978-981-97-7662-7</a>},
    booktitle={Symmetry in Geometry and Analysis, Volume 2}, author={Hilgert, Joachim},
    year={2025} }'
  chicago: Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric
    Spaces.” In <i>Symmetry in Geometry and Analysis, Volume 2</i>, 2025. <a href="https://doi.org/10.1007/978-981-97-7662-7">https://doi.org/10.1007/978-981-97-7662-7</a>.
  ieee: J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces,”
    in <i>Symmetry in Geometry and Analysis, Volume 2</i>, 2025.
  mla: Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric
    Spaces.” <i>Symmetry in Geometry and Analysis, Volume 2</i>, 2025, doi:<a href="https://doi.org/10.1007/978-981-97-7662-7">https://doi.org/10.1007/978-981-97-7662-7</a>.
  short: 'J. Hilgert, in: Symmetry in Geometry and Analysis, Volume 2, 2025.'
date_created: 2025-02-11T17:59:07Z
date_updated: 2025-02-11T18:10:35Z
doi: https://doi.org/10.1007/978-981-97-7662-7
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/chapter/10.1007/978-981-97-7662-7_7
publication: Symmetry in Geometry and Analysis, Volume 2
status: public
title: Quantum-Classical Correspondences for Locally Symmetric Spaces
type: book_chapter
user_id: '220'
year: '2025'
...
---
_id: '53413'
abstract:
- lang: eng
  text: "For negatively curved symmetric spaces it is known that the poles of the\r\nscattering
    matrices defined via the standard intertwining operators for the\r\nspherical
    principal representations of the isometry group are either given as\r\npoles of
    the intertwining operators or as quantum resonances, i.e. poles of the\r\nmeromorphically
    continued resolvents of the Laplace-Beltrami operator. We\r\nextend this result
    to classical locally symmetric spaces of negative curvature\r\nwith convex-cocompact
    fundamental group using results of Bunke and Olbrich. The\r\nmethod of proof forces
    us to exclude the spectral parameters corresponding to\r\nsingular Poisson transforms."
article_type: original
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Delarue B, Hilgert J. Quantum resonances and scattering poles of classical
    rank one locally  symmetric spaces. <i>Journal of Lie Theory</i>. 35((4)):787--804.
  apa: Delarue, B., &#38; Hilgert, J. (n.d.). Quantum resonances and scattering poles
    of classical rank one locally  symmetric spaces. <i>Journal of Lie Theory</i>,
    <i>35</i>((4)), 787--804.
  bibtex: '@article{Delarue_Hilgert, title={Quantum resonances and scattering poles
    of classical rank one locally  symmetric spaces}, volume={35}, number={(4)}, journal={Journal
    of Lie Theory}, author={Delarue, Benjamin and Hilgert, Joachim}, pages={787--804}
    }'
  chicago: 'Delarue, Benjamin, and Joachim Hilgert. “Quantum Resonances and Scattering
    Poles of Classical Rank One Locally  Symmetric Spaces.” <i>Journal of Lie Theory</i>
    35, no. (4) (n.d.): 787--804.'
  ieee: B. Delarue and J. Hilgert, “Quantum resonances and scattering poles of classical
    rank one locally  symmetric spaces,” <i>Journal of Lie Theory</i>, vol. 35, no.
    (4), pp. 787--804.
  mla: Delarue, Benjamin, and Joachim Hilgert. “Quantum Resonances and Scattering
    Poles of Classical Rank One Locally  Symmetric Spaces.” <i>Journal of Lie Theory</i>,
    vol. 35, no. (4), pp. 787--804.
  short: B. Delarue, J. Hilgert, Journal of Lie Theory 35 (n.d.) 787--804.
date_created: 2024-04-11T12:31:18Z
date_updated: 2026-03-31T09:07:17Z
department:
- _id: '548'
intvolume: '        35'
issue: (4)
language:
- iso: eng
page: 787--804
publication: Journal of Lie Theory
publication_identifier:
  issn:
  - 0949-5932
publication_status: inpress
status: public
title: Quantum resonances and scattering poles of classical rank one locally  symmetric
  spaces
type: journal_article
user_id: '220'
volume: 35
year: '2025'
...
---
_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: '60078'
alternative_title:
- From Linear Algebra over Rings to Geometry with Sheaves
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. <i>Mathematical Structures</i>. Springer Berlin Heidelberg; 2024.
    doi:<a href="https://doi.org/10.1007/978-3-662-69412-1">10.1007/978-3-662-69412-1</a>
  apa: Hilgert, J. (2024). <i>Mathematical Structures</i>. Springer Berlin Heidelberg.
    <a href="https://doi.org/10.1007/978-3-662-69412-1">https://doi.org/10.1007/978-3-662-69412-1</a>
  bibtex: '@book{Hilgert_2024, place={Berlin, Heidelberg}, title={Mathematical Structures},
    DOI={<a href="https://doi.org/10.1007/978-3-662-69412-1">10.1007/978-3-662-69412-1</a>},
    publisher={Springer Berlin Heidelberg}, author={Hilgert, Joachim}, year={2024}
    }'
  chicago: 'Hilgert, Joachim. <i>Mathematical Structures</i>. Berlin, Heidelberg:
    Springer Berlin Heidelberg, 2024. <a href="https://doi.org/10.1007/978-3-662-69412-1">https://doi.org/10.1007/978-3-662-69412-1</a>.'
  ieee: 'J. Hilgert, <i>Mathematical Structures</i>. Berlin, Heidelberg: Springer
    Berlin Heidelberg, 2024.'
  mla: Hilgert, Joachim. <i>Mathematical Structures</i>. Springer Berlin Heidelberg,
    2024, doi:<a href="https://doi.org/10.1007/978-3-662-69412-1">10.1007/978-3-662-69412-1</a>.
  short: J. Hilgert, Mathematical Structures, Springer Berlin Heidelberg, Berlin,
    Heidelberg, 2024.
date_created: 2025-05-30T16:11:49Z
date_updated: 2025-05-30T16:12:23Z
doi: 10.1007/978-3-662-69412-1
language:
- iso: eng
place: Berlin, Heidelberg
publication_identifier:
  isbn:
  - '9783662694114'
  - '9783662694121'
  issn:
  - 2731-3824
  - 2731-3832
publication_status: published
publisher: Springer Berlin Heidelberg
status: public
title: Mathematical Structures
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: '57498'
article_number: '105355'
author:
- first_name: Thomas
  full_name: Baier, Thomas
  last_name: Baier
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Oguzhan
  full_name: Kaya, Oguzhan
  last_name: Kaya
- first_name: José M.
  full_name: Mourão, José M.
  last_name: Mourão
- first_name: João P.
  full_name: Nunes, João P.
  last_name: Nunes
citation:
  ama: Baier T, Hilgert J, Kaya O, Mourão JM, Nunes JP. Quantization in fibering polarizations,
    Mabuchi rays and geometric Peter–Weyl theorem. <i>Journal of Geometry and Physics</i>.
    2024;207. doi:<a href="https://doi.org/10.1016/j.geomphys.2024.105355">10.1016/j.geomphys.2024.105355</a>
  apa: Baier, T., Hilgert, J., Kaya, O., Mourão, J. M., &#38; Nunes, J. P. (2024).
    Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl
    theorem. <i>Journal of Geometry and Physics</i>, <i>207</i>, Article 105355. <a
    href="https://doi.org/10.1016/j.geomphys.2024.105355">https://doi.org/10.1016/j.geomphys.2024.105355</a>
  bibtex: '@article{Baier_Hilgert_Kaya_Mourão_Nunes_2024, title={Quantization in fibering
    polarizations, Mabuchi rays and geometric Peter–Weyl theorem}, volume={207}, DOI={<a
    href="https://doi.org/10.1016/j.geomphys.2024.105355">10.1016/j.geomphys.2024.105355</a>},
    number={105355}, journal={Journal of Geometry and Physics}, publisher={Elsevier
    BV}, author={Baier, Thomas and Hilgert, Joachim and Kaya, Oguzhan and Mourão,
    José M. and Nunes, João P.}, year={2024} }'
  chicago: Baier, Thomas, Joachim Hilgert, Oguzhan Kaya, José M. Mourão, and João
    P. Nunes. “Quantization in Fibering Polarizations, Mabuchi Rays and Geometric
    Peter–Weyl Theorem.” <i>Journal of Geometry and Physics</i> 207 (2024). <a href="https://doi.org/10.1016/j.geomphys.2024.105355">https://doi.org/10.1016/j.geomphys.2024.105355</a>.
  ieee: 'T. Baier, J. Hilgert, O. Kaya, J. M. Mourão, and J. P. Nunes, “Quantization
    in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem,” <i>Journal
    of Geometry and Physics</i>, vol. 207, Art. no. 105355, 2024, doi: <a href="https://doi.org/10.1016/j.geomphys.2024.105355">10.1016/j.geomphys.2024.105355</a>.'
  mla: Baier, Thomas, et al. “Quantization in Fibering Polarizations, Mabuchi Rays
    and Geometric Peter–Weyl Theorem.” <i>Journal of Geometry and Physics</i>, vol.
    207, 105355, Elsevier BV, 2024, doi:<a href="https://doi.org/10.1016/j.geomphys.2024.105355">10.1016/j.geomphys.2024.105355</a>.
  short: T. Baier, J. Hilgert, O. Kaya, J.M. Mourão, J.P. Nunes, Journal of Geometry
    and Physics 207 (2024).
date_created: 2024-11-29T09:45:57Z
date_updated: 2025-01-13T15:57:19Z
doi: 10.1016/j.geomphys.2024.105355
intvolume: '       207'
language:
- iso: eng
publication: Journal of Geometry and Physics
publication_identifier:
  issn:
  - 0393-0440
publication_status: published
publisher: Elsevier BV
status: public
title: Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl
  theorem
type: journal_article
user_id: '220'
volume: 207
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: '57590'
alternative_title:
- Von der linearen Algebra über Ringen zur Geometrie mit Garben
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. <i>Mathematische Strukturen 2. Auflage</i>. Springer Berlin Heidelberg;
    2024. doi:<a href="https://doi.org/10.1007/978-3-662-68893-9">10.1007/978-3-662-68893-9</a>
  apa: Hilgert, J. (2024). <i>Mathematische Strukturen 2. Auflage</i>. Springer Berlin
    Heidelberg. <a href="https://doi.org/10.1007/978-3-662-68893-9">https://doi.org/10.1007/978-3-662-68893-9</a>
  bibtex: '@book{Hilgert_2024, place={Berlin, Heidelberg}, title={Mathematische Strukturen
    2. Auflage}, DOI={<a href="https://doi.org/10.1007/978-3-662-68893-9">10.1007/978-3-662-68893-9</a>},
    publisher={Springer Berlin Heidelberg}, author={Hilgert, Joachim}, year={2024}
    }'
  chicago: 'Hilgert, Joachim. <i>Mathematische Strukturen 2. Auflage</i>. Berlin,
    Heidelberg: Springer Berlin Heidelberg, 2024. <a href="https://doi.org/10.1007/978-3-662-68893-9">https://doi.org/10.1007/978-3-662-68893-9</a>.'
  ieee: 'J. Hilgert, <i>Mathematische Strukturen 2. Auflage</i>. Berlin, Heidelberg:
    Springer Berlin Heidelberg, 2024.'
  mla: Hilgert, Joachim. <i>Mathematische Strukturen 2. Auflage</i>. Springer Berlin
    Heidelberg, 2024, doi:<a href="https://doi.org/10.1007/978-3-662-68893-9">10.1007/978-3-662-68893-9</a>.
  short: J. Hilgert, Mathematische Strukturen 2. Auflage, Springer Berlin Heidelberg,
    Berlin, Heidelberg, 2024.
date_created: 2024-12-05T09:09:58Z
date_updated: 2025-01-13T16:08:17Z
doi: 10.1007/978-3-662-68893-9
language:
- iso: ger
place: Berlin, Heidelberg
publication_identifier:
  isbn:
  - '9783662688922'
  - '9783662688939'
publication_status: published
publisher: Springer Berlin Heidelberg
status: public
title: Mathematische Strukturen 2. Auflage
type: book
user_id: '220'
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'
...
---
_id: '34793'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Glöckner H, Hilgert J. Aspects of control theory on infinite-dimensional Lie
    groups and G-manifolds. <i>Journal of Differential Equations</i>. 2023;343:186–232.
    doi:<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>
  apa: Glöckner, H., &#38; Hilgert, J. (2023). Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds. <i>Journal of Differential Equations</i>, <i>343</i>,
    186–232. <a href="https://doi.org/10.1016/j.jde.2022.10.001">https://doi.org/10.1016/j.jde.2022.10.001</a>
  bibtex: '@article{Glöckner_Hilgert_2023, title={Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds}, volume={343}, DOI={<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>},
    journal={Journal of Differential Equations}, author={Glöckner, Helge and Hilgert,
    Joachim}, year={2023}, pages={186–232} }'
  chicago: 'Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional
    Lie Groups and G-Manifolds.” <i>Journal of Differential Equations</i> 343 (2023):
    186–232. <a href="https://doi.org/10.1016/j.jde.2022.10.001">https://doi.org/10.1016/j.jde.2022.10.001</a>.'
  ieee: 'H. Glöckner and J. Hilgert, “Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds,” <i>Journal of Differential Equations</i>, vol. 343,
    pp. 186–232, 2023, doi: <a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>.'
  mla: Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional
    Lie Groups and G-Manifolds.” <i>Journal of Differential Equations</i>, vol. 343,
    2023, pp. 186–232, doi:<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>.
  short: H. Glöckner, J. Hilgert, Journal of Differential Equations 343 (2023) 186–232.
date_created: 2022-12-21T19:31:13Z
date_updated: 2024-03-22T16:02:32Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
- _id: '91'
doi: 10.1016/j.jde.2022.10.001
external_id:
  arxiv:
  - '2007.11277'
intvolume: '       343'
keyword:
- '22E65'
- 28B05
- 34A12
- 34H05
- '46E30'
- '46E40'
language:
- iso: eng
page: 186–232
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
quality_controlled: '1'
status: public
title: Aspects of control theory on infinite-dimensional Lie groups and G-manifolds
type: journal_article
user_id: '178'
volume: 343
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: '51383'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: C.
  full_name: Arends, C.
  last_name: Arends
citation:
  ama: Hilgert J, Arends C. Spectral correspondences for rank one locally symmetric
    spaces - The case of exceptional parameters. <i>J de l’École polytechnique — Mathématiques</i>.
    2023;10:335-403.
  apa: Hilgert, J., &#38; Arends, C. (2023). Spectral correspondences for rank one
    locally symmetric spaces - The case of exceptional parameters. <i>J. de l’École
    Polytechnique — Mathématiques</i>, <i>10</i>, 335–403.
  bibtex: '@article{Hilgert_Arends_2023, title={Spectral correspondences for rank
    one locally symmetric spaces - The case of exceptional parameters}, volume={10},
    journal={J. de l’École polytechnique — Mathématiques}, author={Hilgert, Joachim
    and Arends, C.}, year={2023}, pages={335–403} }'
  chicago: 'Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One
    Locally Symmetric Spaces - The Case of Exceptional Parameters.” <i>J. de l’École
    Polytechnique — Mathématiques</i> 10 (2023): 335–403.'
  ieee: J. Hilgert and C. Arends, “Spectral correspondences for rank one locally symmetric
    spaces - The case of exceptional parameters,” <i>J. de l’École polytechnique —
    Mathématiques</i>, vol. 10, pp. 335–403, 2023.
  mla: Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One Locally
    Symmetric Spaces - The Case of Exceptional Parameters.” <i>J. de l’École Polytechnique
    — Mathématiques</i>, vol. 10, 2023, pp. 335–403.
  short: J. Hilgert, C. Arends, J. de l’École Polytechnique — Mathématiques 10 (2023)
    335–403.
date_created: 2024-02-19T06:34:11Z
date_updated: 2026-03-31T08:26:09Z
department:
- _id: '91'
intvolume: '        10'
language:
- iso: eng
page: 335-403
publication: J. de l'École polytechnique — Mathématiques
publication_status: published
status: public
title: Spectral correspondences for rank one locally symmetric spaces - The case of
  exceptional parameters
type: journal_article
user_id: '220'
volume: 10
year: '2023'
...
---
_id: '51384'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: H.
  full_name: Glöckner, H.
  last_name: Glöckner
citation:
  ama: Hilgert J, Glöckner H. Aspects of control theory on infinite-dimensional Lie
    groups and G-manifolds. <i>J Diff Equations</i>. 2023;343:186-232.
  apa: Hilgert, J., &#38; Glöckner, H. (2023). Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds. <i>J. Diff. Equations</i>, <i>343</i>, 186–232.
  bibtex: '@article{Hilgert_Glöckner_2023, title={Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds}, volume={343}, journal={J. Diff. Equations}, author={Hilgert,
    Joachim and Glöckner, H.}, year={2023}, pages={186–232} }'
  chicago: 'Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional
    Lie Groups and G-Manifolds.” <i>J. Diff. Equations</i> 343 (2023): 186–232.'
  ieee: J. Hilgert and H. Glöckner, “Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds,” <i>J. Diff. Equations</i>, vol. 343, pp. 186–232,
    2023.
  mla: Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional
    Lie Groups and G-Manifolds.” <i>J. Diff. Equations</i>, vol. 343, 2023, pp. 186–232.
  short: J. Hilgert, H. Glöckner, J. Diff. Equations 343 (2023) 186–232.
date_created: 2024-02-19T06:35:08Z
date_updated: 2026-03-31T08:25:53Z
department:
- _id: '91'
intvolume: '       343'
language:
- iso: eng
page: 186-232
publication: J. Diff. Equations
publication_status: published
status: public
title: Aspects of control theory on infinite-dimensional Lie groups and G-manifolds
type: journal_article
user_id: '220'
volume: 343
year: '2023'
...
---
_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: '51554'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: 'Hilgert J. Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second
    Edition. AMS/MAA Press 2021. <i>Mathematische Semesterberichte</i>. 2022;69:151–153.
    doi:<a href="https://doi.org/10.1007/s00591-021-00314-7">10.1007/s00591-021-00314-7</a>'
  apa: 'Hilgert, J. (2022). Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics,
    Second Edition. AMS/MAA Press 2021. In <i>Mathematische Semesterberichte</i> (Vol.
    69, pp. 151–153). <a href="https://doi.org/10.1007/s00591-021-00314-7">https://doi.org/10.1007/s00591-021-00314-7</a>'
  bibtex: '@article{Hilgert_2022, title={Ethan D. Bolker und Maura B. Mast: Common
    Sense Mathematics, Second Edition. AMS/MAA Press 2021}, volume={69}, DOI={<a href="https://doi.org/10.1007/s00591-021-00314-7">10.1007/s00591-021-00314-7</a>},
    journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2022},
    pages={151–153} }'
  chicago: 'Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics,
    Second Edition. AMS/MAA Press 2021.” <i>Mathematische Semesterberichte</i>, 2022.
    <a href="https://doi.org/10.1007/s00591-021-00314-7">https://doi.org/10.1007/s00591-021-00314-7</a>.'
  ieee: 'J. Hilgert, “Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics,
    Second Edition. AMS/MAA Press 2021,” <i>Mathematische Semesterberichte</i>, vol.
    69. pp. 151–153, 2022, doi: <a href="https://doi.org/10.1007/s00591-021-00314-7">10.1007/s00591-021-00314-7</a>.'
  mla: 'Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics,
    Second Edition. AMS/MAA Press 2021.” <i>Mathematische Semesterberichte</i>, vol.
    69, 2022, pp. 151–153, doi:<a href="https://doi.org/10.1007/s00591-021-00314-7">10.1007/s00591-021-00314-7</a>.'
  short: J. Hilgert, Mathematische Semesterberichte 69 (2022) 151–153.
date_created: 2024-02-20T09:49:04Z
date_updated: 2024-02-20T09:52:53Z
department:
- _id: '91'
doi: 10.1007/s00591-021-00314-7
intvolume: '        69'
language:
- iso: eng
page: 151–153
publication: Mathematische Semesterberichte
publication_status: published
status: public
title: 'Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition.
  AMS/MAA Press 2021'
type: review
user_id: '49063'
volume: 69
year: '2022'
...