---
_id: '34833'
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. Decompositions of Analytic 1-Manifolds. <i>Indagationes Mathematicae</i>.
    2023;34(4):752-811. doi:<a href="https://doi.org/10.1016/j.indag.2023.02.003">10.1016/j.indag.2023.02.003</a>
  apa: Hanusch, M. (2023). Decompositions of Analytic 1-Manifolds. <i>Indagationes
    Mathematicae.</i>, <i>34</i>(4), 752–811. <a href="https://doi.org/10.1016/j.indag.2023.02.003">https://doi.org/10.1016/j.indag.2023.02.003</a>
  bibtex: '@article{Hanusch_2023, title={Decompositions of Analytic 1-Manifolds},
    volume={34}, DOI={<a href="https://doi.org/10.1016/j.indag.2023.02.003">10.1016/j.indag.2023.02.003</a>},
    number={4}, journal={Indagationes Mathematicae.}, author={Hanusch, Maximilian},
    year={2023}, pages={752–811} }'
  chicago: 'Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” <i>Indagationes
    Mathematicae.</i> 34, no. 4 (2023): 752–811. <a href="https://doi.org/10.1016/j.indag.2023.02.003">https://doi.org/10.1016/j.indag.2023.02.003</a>.'
  ieee: 'M. Hanusch, “Decompositions of Analytic 1-Manifolds,” <i>Indagationes Mathematicae.</i>,
    vol. 34, no. 4, pp. 752–811, 2023, doi: <a href="https://doi.org/10.1016/j.indag.2023.02.003">10.1016/j.indag.2023.02.003</a>.'
  mla: Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” <i>Indagationes
    Mathematicae.</i>, vol. 34, no. 4, 2023, pp. 752–811, doi:<a href="https://doi.org/10.1016/j.indag.2023.02.003">10.1016/j.indag.2023.02.003</a>.
  short: M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.
date_created: 2022-12-22T09:46:36Z
date_updated: 2023-05-25T07:32:38Z
department:
- _id: '93'
doi: 10.1016/j.indag.2023.02.003
intvolume: '        34'
issue: '4'
keyword:
- Lie group actions and analytic 1-submanifolds
language:
- iso: eng
page: 752-811
publication: Indagationes Mathematicae.
publication_status: published
status: public
title: Decompositions of Analytic 1-Manifolds
type: journal_article
user_id: '30905'
volume: 34
year: '2023'
...
---
_id: '63635'
article_type: original
author:
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Oliver
  full_name: Matte, Oliver
  last_name: Matte
citation:
  ama: Hinrichs B, Matte O. Feynman–Kac Formula and Asymptotic Behavior of the Minimal
    Energy for the Relativistic Nelson Model in Two Spatial Dimensions. <i>Annales
    Henri Poincaré</i>. 2023;25(6):2877-2940. doi:<a href="https://doi.org/10.1007/s00023-023-01369-z">10.1007/s00023-023-01369-z</a>
  apa: Hinrichs, B., &#38; Matte, O. (2023). Feynman–Kac Formula and Asymptotic Behavior
    of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.
    <i>Annales Henri Poincaré</i>, <i>25</i>(6), 2877–2940. <a href="https://doi.org/10.1007/s00023-023-01369-z">https://doi.org/10.1007/s00023-023-01369-z</a>
  bibtex: '@article{Hinrichs_Matte_2023, title={Feynman–Kac Formula and Asymptotic
    Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial
    Dimensions}, volume={25}, DOI={<a href="https://doi.org/10.1007/s00023-023-01369-z">10.1007/s00023-023-01369-z</a>},
    number={6}, journal={Annales Henri Poincaré}, publisher={Springer Science and
    Business Media LLC}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2023},
    pages={2877–2940} }'
  chicago: 'Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic
    Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial
    Dimensions.” <i>Annales Henri Poincaré</i> 25, no. 6 (2023): 2877–2940. <a href="https://doi.org/10.1007/s00023-023-01369-z">https://doi.org/10.1007/s00023-023-01369-z</a>.'
  ieee: 'B. Hinrichs and O. Matte, “Feynman–Kac Formula and Asymptotic Behavior of
    the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions,”
    <i>Annales Henri Poincaré</i>, vol. 25, no. 6, pp. 2877–2940, 2023, doi: <a href="https://doi.org/10.1007/s00023-023-01369-z">10.1007/s00023-023-01369-z</a>.'
  mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic Behavior
    of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.”
    <i>Annales Henri Poincaré</i>, vol. 25, no. 6, Springer Science and Business Media
    LLC, 2023, pp. 2877–940, doi:<a href="https://doi.org/10.1007/s00023-023-01369-z">10.1007/s00023-023-01369-z</a>.
  short: B. Hinrichs, O. Matte, Annales Henri Poincaré 25 (2023) 2877–2940.
date_created: 2026-01-16T08:39:40Z
date_updated: 2026-01-16T09:05:26Z
department:
- _id: '799'
doi: 10.1007/s00023-023-01369-z
extern: '1'
external_id:
  arxiv:
  - '2211.14046'
intvolume: '        25'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 2877-2940
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic
  Nelson Model in Two Spatial Dimensions
type: journal_article
user_id: '99427'
volume: 25
year: '2023'
...
---
_id: '46100'
article_number: '127558'
author:
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Daan W.
  full_name: Janssen, Daan W.
  last_name: Janssen
- first_name: Jobst
  full_name: Ziebell, Jobst
  last_name: Ziebell
citation:
  ama: 'Hinrichs B, Janssen DW, Ziebell J. Super-Gaussian decay of exponentials: A
    sufficient condition. <i>Journal of Mathematical Analysis and Applications</i>.
    2023;528(1). doi:<a href="https://doi.org/10.1016/j.jmaa.2023.127558">10.1016/j.jmaa.2023.127558</a>'
  apa: 'Hinrichs, B., Janssen, D. W., &#38; Ziebell, J. (2023). Super-Gaussian decay
    of exponentials: A sufficient condition. <i>Journal of Mathematical Analysis and
    Applications</i>, <i>528</i>(1), Article 127558. <a href="https://doi.org/10.1016/j.jmaa.2023.127558">https://doi.org/10.1016/j.jmaa.2023.127558</a>'
  bibtex: '@article{Hinrichs_Janssen_Ziebell_2023, title={Super-Gaussian decay of
    exponentials: A sufficient condition}, volume={528}, DOI={<a href="https://doi.org/10.1016/j.jmaa.2023.127558">10.1016/j.jmaa.2023.127558</a>},
    number={1127558}, journal={Journal of Mathematical Analysis and Applications},
    publisher={Elsevier BV}, author={Hinrichs, Benjamin and Janssen, Daan W. and Ziebell,
    Jobst}, year={2023} }'
  chicago: 'Hinrichs, Benjamin, Daan W. Janssen, and Jobst Ziebell. “Super-Gaussian
    Decay of Exponentials: A Sufficient Condition.” <i>Journal of Mathematical Analysis
    and Applications</i> 528, no. 1 (2023). <a href="https://doi.org/10.1016/j.jmaa.2023.127558">https://doi.org/10.1016/j.jmaa.2023.127558</a>.'
  ieee: 'B. Hinrichs, D. W. Janssen, and J. Ziebell, “Super-Gaussian decay of exponentials:
    A sufficient condition,” <i>Journal of Mathematical Analysis and Applications</i>,
    vol. 528, no. 1, Art. no. 127558, 2023, doi: <a href="https://doi.org/10.1016/j.jmaa.2023.127558">10.1016/j.jmaa.2023.127558</a>.'
  mla: 'Hinrichs, Benjamin, et al. “Super-Gaussian Decay of Exponentials: A Sufficient
    Condition.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 528,
    no. 1, 127558, Elsevier BV, 2023, doi:<a href="https://doi.org/10.1016/j.jmaa.2023.127558">10.1016/j.jmaa.2023.127558</a>.'
  short: B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and
    Applications 528 (2023).
date_created: 2023-07-20T05:08:49Z
date_updated: 2026-01-16T09:04:39Z
department:
- _id: '799'
doi: 10.1016/j.jmaa.2023.127558
external_id:
  arxiv:
  - '2205.09189'
intvolume: '       528'
issue: '1'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication: Journal of Mathematical Analysis and Applications
publication_identifier:
  issn:
  - 0022-247X
publication_status: published
publisher: Elsevier BV
status: public
title: 'Super-Gaussian decay of exponentials: A sufficient condition'
type: journal_article
user_id: '99427'
volume: 528
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: '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: '31982'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>We show that for a generic conformal
    metric perturbation of a compact hyperbolic 3-manifold <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    with Betti number <jats:inline-formula><jats:alternatives><jats:tex-math>$$b_1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n
    \                   <mml:mi>b</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n
    \                 </mml:msub>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    the order of vanishing of the Ruelle zeta function at zero equals <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-b_1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n
    \                   <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n
    \                     <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    while in the hyperbolic case it is equal to <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-2b_1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n
    \                   <mml:mn>2</mml:mn>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n
    \                     <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.
    This is in contrast to the 2-dimensional case where the order of vanishing is
    a topological invariant. The proof uses the microlocal approach to dynamical zeta
    functions, giving a geometric description of generalized Pollicott–Ruelle resonant
    differential forms at 0 in the hyperbolic case and using first variation for the
    perturbation. To show that the first variation is generically nonzero we introduce
    a new identity relating pushforwards of products of resonant and coresonant 2-forms
    on the sphere bundle <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\\Sigma
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>Σ</mml:mi>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    with harmonic 1-forms on <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>"
author:
- first_name: Mihajlo
  full_name: Cekić, Mihajlo
  last_name: Cekić
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Semyon
  full_name: Dyatlov, Semyon
  last_name: Dyatlov
- first_name: Gabriel P.
  full_name: Paternain, Gabriel P.
  last_name: Paternain
citation:
  ama: Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero
    for nearly hyperbolic 3-manifolds. <i>Inventiones mathematicae</i>. 2022;229(1):303-394.
    doi:<a href="https://doi.org/10.1007/s00222-022-01108-x">10.1007/s00222-022-01108-x</a>
  apa: Cekić, M., Delarue, B., Dyatlov, S., &#38; Paternain, G. P. (2022). The Ruelle
    zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones Mathematicae</i>,
    <i>229</i>(1), 303–394. <a href="https://doi.org/10.1007/s00222-022-01108-x">https://doi.org/10.1007/s00222-022-01108-x</a>
  bibtex: '@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function
    at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={<a href="https://doi.org/10.1007/s00222-022-01108-x">10.1007/s00222-022-01108-x</a>},
    number={1}, journal={Inventiones mathematicae}, publisher={Springer Science and
    Business Media LLC}, author={Cekić, Mihajlo and Delarue, Benjamin and Dyatlov,
    Semyon and Paternain, Gabriel P.}, year={2022}, pages={303–394} }'
  chicago: 'Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain.
    “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones
    Mathematicae</i> 229, no. 1 (2022): 303–94. <a href="https://doi.org/10.1007/s00222-022-01108-x">https://doi.org/10.1007/s00222-022-01108-x</a>.'
  ieee: 'M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function
    at zero for nearly hyperbolic 3-manifolds,” <i>Inventiones mathematicae</i>, vol.
    229, no. 1, pp. 303–394, 2022, doi: <a href="https://doi.org/10.1007/s00222-022-01108-x">10.1007/s00222-022-01108-x</a>.'
  mla: Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic
    3-Manifolds.” <i>Inventiones Mathematicae</i>, vol. 229, no. 1, Springer Science
    and Business Media LLC, 2022, pp. 303–94, doi:<a href="https://doi.org/10.1007/s00222-022-01108-x">10.1007/s00222-022-01108-x</a>.
  short: M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae
    229 (2022) 303–394.
date_created: 2022-06-20T08:24:17Z
date_updated: 2022-06-21T11:55:15Z
department:
- _id: '548'
doi: 10.1007/s00222-022-01108-x
intvolume: '       229'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 303-394
publication: Inventiones mathematicae
publication_identifier:
  issn:
  - 0020-9910
  - 1432-1297
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
type: journal_article
user_id: '70575'
volume: 229
year: '2022'
...
---
_id: '34792'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Non-Lie subgroups in Lie groups over local fields of positive characteristic.
    <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>. 2022;14(2):138–144.
    doi:<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>
  apa: Glöckner, H. (2022). Non-Lie subgroups in Lie groups over local fields of positive
    characteristic. <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    <i>14</i>(2), 138–144. <a href="https://doi.org/10.1134/S2070046622020042">https://doi.org/10.1134/S2070046622020042</a>
  bibtex: '@article{Glöckner_2022, title={Non-Lie subgroups in Lie groups over local
    fields of positive characteristic}, volume={14}, DOI={<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>},
    number={2}, journal={p-Adic Numbers, Ultrametric Analysis, and Applications},
    author={Glöckner, Helge}, year={2022}, pages={138–144} }'
  chicago: 'Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of
    Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>
    14, no. 2 (2022): 138–144. <a href="https://doi.org/10.1134/S2070046622020042">https://doi.org/10.1134/S2070046622020042</a>.'
  ieee: 'H. Glöckner, “Non-Lie subgroups in Lie groups over local fields of positive
    characteristic,” <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    vol. 14, no. 2, pp. 138–144, 2022, doi: <a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>.'
  mla: Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive
    Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    vol. 14, no. 2, 2022, pp. 138–144, doi:<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>.
  short: H. Glöckner, P-Adic Numbers, Ultrametric Analysis, and Applications 14 (2022)
    138–144.
date_created: 2022-12-21T19:27:51Z
date_updated: 2022-12-21T19:30:25Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1134/S2070046622020042
intvolume: '        14'
issue: '2'
keyword:
- 20Exx
- 22Exx
- 32Cxx
language:
- iso: eng
page: 138–144
publication: p-Adic Numbers, Ultrametric Analysis, and Applications
publication_identifier:
  issn:
  - 2070-0466
quality_controlled: '1'
status: public
title: Non-Lie subgroups in Lie groups over local fields of positive characteristic
type: journal_article
user_id: '178'
volume: 14
year: '2022'
...
---
_id: '34791'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Alexander
  full_name: Schmeding, Alexander
  last_name: Schmeding
citation:
  ama: Glöckner H, Schmeding A. Manifolds of mappings on Cartesian products. <i>Annals
    of Global Analysis and Geometry</i>. 2022;61(2):359–398. doi:<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>
  apa: Glöckner, H., &#38; Schmeding, A. (2022). Manifolds of mappings on Cartesian
    products. <i>Annals of Global Analysis and Geometry</i>, <i>61</i>(2), 359–398.
    <a href="https://doi.org/10.1007/s10455-021-09816-y">https://doi.org/10.1007/s10455-021-09816-y</a>
  bibtex: '@article{Glöckner_Schmeding_2022, title={Manifolds of mappings on Cartesian
    products}, volume={61}, DOI={<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>},
    number={2}, journal={Annals of Global Analysis and Geometry}, author={Glöckner,
    Helge and Schmeding, Alexander}, year={2022}, pages={359–398} }'
  chicago: 'Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian
    Products.” <i>Annals of Global Analysis and Geometry</i> 61, no. 2 (2022): 359–398.
    <a href="https://doi.org/10.1007/s10455-021-09816-y">https://doi.org/10.1007/s10455-021-09816-y</a>.'
  ieee: 'H. Glöckner and A. Schmeding, “Manifolds of mappings on Cartesian products,”
    <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, pp. 359–398, 2022,
    doi: <a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>.'
  mla: Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian
    Products.” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, 2022,
    pp. 359–398, doi:<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>.
  short: H. Glöckner, A. Schmeding, Annals of Global Analysis and Geometry 61 (2022)
    359–398.
date_created: 2022-12-21T19:24:48Z
date_updated: 2022-12-21T19:27:09Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1007/s10455-021-09816-y
intvolume: '        61'
issue: '2'
keyword:
- 58D15
- '22E65'
- '26E15'
- '26E20'
- '46E40'
- 46T20
- 58A05
language:
- iso: eng
page: 359–398
publication: Annals of Global Analysis and Geometry
publication_identifier:
  issn:
  - 0232-704X
quality_controlled: '1'
status: public
title: Manifolds of mappings on Cartesian products
type: journal_article
user_id: '178'
volume: 61
year: '2022'
...
---
_id: '34796'
abstract:
- lang: eng
  text: 'We prove various results in infinite-dimensional differential calculus that
    relate the differentiability properties of functions and associated operator-valued
    functions (e.g., differentials). The results are applied in two areas: (1) in
    the theory of infinite-dimensional vector bundles, to construct new bundles from
    given ones, such as dual bundles, topological tensor products, infinite direct
    sums, and completions (under suitable hypotheses); (2) in the theory of locally
    convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity
    of passage from a function to the associated Hamiltonian vector field. Topological
    properties of topological vector spaces are essential for the studies, which allow
    the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter
    kR-spaces and locally convex spaces E such that E&times;E is a kR-space.'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces. <i>Axioms</i>. 2022;11(5). doi:<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>
  apa: Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces. <i>Axioms</i>, <i>11</i>(5). <a href="https://doi.org/10.3390/axioms11050221">https://doi.org/10.3390/axioms11050221</a>
  bibtex: '@article{Glöckner_2022, title={Aspects of differential calculus related
    to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11},
    DOI={<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>},
    number={5}, journal={Axioms}, author={Glöckner, Helge}, year={2022} }'
  chicago: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
    Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i> 11, no. 5 (2022). <a
    href="https://doi.org/10.3390/axioms11050221">https://doi.org/10.3390/axioms11050221</a>.
  ieee: 'H. Glöckner, “Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces,” <i>Axioms</i>, vol. 11, no. 5, 2022,
    doi: <a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>.'
  mla: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
    Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i>, vol. 11, no. 5, 2022,
    doi:<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>.
  short: H. Glöckner, Axioms 11 (2022).
date_created: 2022-12-21T20:02:29Z
date_updated: 2022-12-22T07:31:55Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.3390/axioms11050221
intvolume: '        11'
issue: '5'
language:
- iso: eng
publication: Axioms
publication_identifier:
  issn:
  - 2075-1680
quality_controlled: '1'
status: public
title: Aspects of differential calculus related to infinite-dimensional vector bundles
  and Poisson vector spaces
type: journal_article
user_id: '178'
volume: 11
year: '2022'
...
---
_id: '34804'
abstract:
- lang: eng
  text: "Starting with a finite-dimensional complex Lie algebra, we extend scalars\r\nusing
    suitable commutative topological algebras. We study Birkhoff\r\ndecompositions
    for the corresponding loop groups. Some results remain valid for\r\nloop groups
    with valued in complex Banach-Lie groups."
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Birkhoff decompositions for loop groups with coefficient algebras.
    <i>arXiv:220611711</i>. Published online 2022.
  apa: Glöckner, H. (2022). Birkhoff decompositions for loop groups with coefficient
    algebras. In <i>arXiv:2206.11711</i>.
  bibtex: '@article{Glöckner_2022, title={Birkhoff decompositions for loop groups
    with coefficient algebras}, journal={arXiv:2206.11711}, author={Glöckner, Helge},
    year={2022} }'
  chicago: Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient
    Algebras.” <i>ArXiv:2206.11711</i>, 2022.
  ieee: H. Glöckner, “Birkhoff decompositions for loop groups with coefficient algebras,”
    <i>arXiv:2206.11711</i>. 2022.
  mla: Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient
    Algebras.” <i>ArXiv:2206.11711</i>, 2022.
  short: H. Glöckner, ArXiv:2206.11711 (2022).
date_created: 2022-12-22T07:42:07Z
date_updated: 2022-12-22T07:44:08Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - '2206.11711'
language:
- iso: eng
publication: arXiv:2206.11711
status: public
title: Birkhoff decompositions for loop groups with coefficient algebras
type: preprint
user_id: '178'
year: '2022'
...
---
_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: '34817'
article_type: original
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. Regularity of Lie groups. <i>Communications in Analysis and Geometry</i>.
    2022;30(1):53-152. doi:<a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">10.4310/cag.2022.v30.n1.a2</a>
  apa: Hanusch, M. (2022). Regularity of Lie groups. <i>Communications in Analysis
    and Geometry</i>, <i>30</i>(1), 53–152. <a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>
  bibtex: '@article{Hanusch_2022, title={Regularity of Lie groups}, volume={30}, DOI={<a
    href="https://doi.org/10.4310/cag.2022.v30.n1.a2">10.4310/cag.2022.v30.n1.a2</a>},
    number={1}, journal={Communications in Analysis and Geometry}, publisher={International
    Press of Boston}, author={Hanusch, Maximilian}, year={2022}, pages={53–152} }'
  chicago: 'Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in
    Analysis and Geometry</i> 30, no. 1 (2022): 53–152. <a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>.'
  ieee: 'M. Hanusch, “Regularity of Lie groups,” <i>Communications in Analysis and
    Geometry</i>, vol. 30, no. 1, pp. 53–152, 2022, doi: <a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">10.4310/cag.2022.v30.n1.a2</a>.'
  mla: Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in Analysis
    and Geometry</i>, vol. 30, no. 1, International Press of Boston, 2022, pp. 53–152,
    doi:<a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">10.4310/cag.2022.v30.n1.a2</a>.
  short: M. Hanusch, Communications in Analysis and Geometry 30 (2022) 53–152.
date_created: 2022-12-22T09:19:43Z
date_updated: 2023-01-09T18:07:30Z
department:
- _id: '93'
doi: 10.4310/cag.2022.v30.n1.a2
extern: '1'
intvolume: '        30'
issue: '1'
keyword:
- regularity of Lie groups
language:
- iso: eng
page: 53-152
publication: Communications in Analysis and Geometry
publication_identifier:
  issn:
  - 1019-8385
  - 1944-9992
publication_status: published
publisher: International Press of Boston
status: public
title: Regularity of Lie groups
type: journal_article
user_id: '30905'
volume: 30
year: '2022'
...
---
_id: '34856'
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching
  apa: Hanusch, M. (n.d.). <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
  bibtex: '@book{Hanusch, title={Analysis 1 und 2 Skript/Buch}, publisher={https://maximilianhanusch.wixsite.com/my-site/lehre-teaching},
    author={Hanusch, Maximilian} }'
  chicago: Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching,
    n.d.
  ieee: M. Hanusch, <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
  mla: Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
  short: M. Hanusch, Analysis 1 und 2 Skript/Buch, https://maximilianhanusch.wixsite.com/my-site/lehre-teaching,
    n.d.
date_created: 2022-12-22T17:06:02Z
date_updated: 2023-01-09T18:07:00Z
department:
- _id: '93'
language:
- iso: ger
page: '385'
publication_status: draft
publisher: https://maximilianhanusch.wixsite.com/my-site/lehre-teaching
status: public
title: Analysis 1 und 2 Skript/Buch
type: working_paper
user_id: '30905'
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: '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'
...
---
_id: '35528'
author:
- first_name: Johannes
  full_name: Lankeit, Johannes
  last_name: Lankeit
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Lankeit J, Winkler M. Radial solutions to a chemotaxis-consumption model involving
    prescribed signal concentrations on the boundary. <i>Nonlinearity</i>. 2022;35:719-749.
  apa: Lankeit, J., &#38; Winkler, M. (2022). Radial solutions to a chemotaxis-consumption
    model involving prescribed signal concentrations on the boundary. <i>Nonlinearity</i>,
    <i>35</i>, 719–749.
  bibtex: '@article{Lankeit_Winkler_2022, title={Radial solutions to a chemotaxis-consumption
    model involving prescribed signal concentrations on the boundary}, volume={35},
    journal={Nonlinearity}, author={Lankeit, Johannes and Winkler, Michael}, year={2022},
    pages={719–749} }'
  chicago: 'Lankeit, Johannes, and Michael Winkler. “Radial Solutions to a Chemotaxis-Consumption
    Model Involving Prescribed Signal Concentrations on the Boundary.” <i>Nonlinearity</i>
    35 (2022): 719–49.'
  ieee: J. Lankeit and M. Winkler, “Radial solutions to a chemotaxis-consumption model
    involving prescribed signal concentrations on the boundary,” <i>Nonlinearity</i>,
    vol. 35, pp. 719–749, 2022.
  mla: Lankeit, Johannes, and Michael Winkler. “Radial Solutions to a Chemotaxis-Consumption
    Model Involving Prescribed Signal Concentrations on the Boundary.” <i>Nonlinearity</i>,
    vol. 35, 2022, pp. 719–49.
  short: J. Lankeit, M. Winkler, Nonlinearity 35 (2022) 719–749.
date_created: 2023-01-09T15:33:38Z
date_updated: 2023-01-20T13:18:15Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: '        35'
language:
- iso: eng
page: 719-749
publication: Nonlinearity
status: public
title: Radial solutions to a chemotaxis-consumption model involving prescribed signal
  concentrations on the boundary
type: journal_article
user_id: '15645'
volume: 35
year: '2022'
...
---
_id: '35568'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes
    interaction. <i>Communications in Mathematical Physics</i>. 2022;389:439-489.
  apa: Winkler, M. (2022). Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes
    interaction. <i>Communications in Mathematical Physics</i>, <i>389</i>, 439–489.
  bibtex: '@article{Winkler_2022, title={Reaction-driven relaxation in threee-dimensional
    Keller-Segel-Navier-Stokes interaction.}, volume={389}, journal={Communications
    in Mathematical Physics}, author={Winkler, Michael}, year={2022}, pages={439–489}
    }'
  chicago: 'Winkler, Michael. “Reaction-Driven Relaxation in Threee-Dimensional Keller-Segel-Navier-Stokes
    Interaction.” <i>Communications in Mathematical Physics</i> 389 (2022): 439–89.'
  ieee: M. Winkler, “Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes
    interaction.,” <i>Communications in Mathematical Physics</i>, vol. 389, pp. 439–489,
    2022.
  mla: Winkler, Michael. “Reaction-Driven Relaxation in Threee-Dimensional Keller-Segel-Navier-Stokes
    Interaction.” <i>Communications in Mathematical Physics</i>, vol. 389, 2022, pp.
    439–89.
  short: M. Winkler, Communications in Mathematical Physics 389 (2022) 439–489.
date_created: 2023-01-09T16:32:21Z
date_updated: 2023-01-20T13:17:37Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: '       389'
language:
- iso: eng
page: 439-489
publication: Communications in Mathematical Physics
status: public
title: Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes
  interaction.
type: journal_article
user_id: '15645'
volume: 389
year: '2022'
...