---
_id: '51204'
abstract:
- lang: eng
text: "Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup
$\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup
$\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant
differential operators, and the decay of matrix coefficients. In\r\nparticular,
this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash
G)$ in this general setting."
author:
- first_name: Christopher
full_name: Lutsko, Christopher
last_name: Lutsko
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
orcid: 0000-0001-8893-2045
citation:
ama: Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness
of locally symmetric spaces. Duke Math Journal . 2026;(to appear).
apa: Lutsko, C., Weich, T., & Wolf, L. L. (2026). Polyhedral bounds on the joint
spectrum and temperedness of locally symmetric spaces. Duke Math. Journal
, (to appear).
bibtex: '@article{Lutsko_Weich_Wolf_2026, title={Polyhedral bounds on the joint
spectrum and temperedness of locally symmetric spaces}, volume={(to appear)},
journal={Duke Math. Journal }, author={Lutsko, Christopher and Weich, Tobias and
Wolf, Lasse Lennart}, year={2026} }'
chicago: Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral
Bounds on the Joint Spectrum and Temperedness of Locally Symmetric Spaces.” Duke
Math. Journal (to appear) (2026).
ieee: C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum
and temperedness of locally symmetric spaces,” Duke Math. Journal , vol.
(to appear), 2026.
mla: Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness
of Locally Symmetric Spaces.” Duke Math. Journal , vol. (to appear), 2026.
short: C. Lutsko, T. Weich, L.L. Wolf, Duke Math. Journal (to appear) (2026).
date_created: 2024-02-06T20:35:36Z
date_updated: 2026-02-18T10:37:47Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
arxiv:
- '2402.02530'
language:
- iso: eng
publication: 'Duke Math. Journal '
status: public
title: Polyhedral bounds on the joint spectrum and temperedness of locally symmetric
spaces
type: journal_article
user_id: '49178'
volume: (to appear)
year: '2026'
...
---
_id: '64569'
abstract:
- lang: eng
text: "Abstract\r\n We show how
the Fourier transform for distributional sections of vector bundles over symmetric
spaces of non‐compact type can be used for questions of solvability of systems
of invariant differential equations in analogy to Hörmander's proof of the Ehrenpreis–Malgrange
theorem. We get complete solvability for the hyperbolic plane and partial results
for products and the hyperbolic 3‐space ."
author:
- first_name: Martin
full_name: Olbrich, Martin
last_name: Olbrich
- first_name: Guendalina
full_name: Palmirotta, Guendalina
id: '109467'
last_name: Palmirotta
citation:
ama: Olbrich M, Palmirotta G. Solvability of invariant systems of differential equations on
H2$\mathbb {H}^2$ and beyond. Mathematische Nachrichten. 2026;299(2):456-479.
doi:10.1002/mana.70100
apa: Olbrich, M., & Palmirotta, G. (2026). Solvability of invariant systems
of differential equations on H2$\mathbb {H}^2$ and beyond. Mathematische Nachrichten,
299(2), 456–479. https://doi.org/10.1002/mana.70100
bibtex: '@article{Olbrich_Palmirotta_2026, title={Solvability of invariant systems
of differential equations on H2$\mathbb {H}^2$ and beyond}, volume={299}, DOI={10.1002/mana.70100}, number={2},
journal={Mathematische Nachrichten}, publisher={Wiley}, author={Olbrich, Martin
and Palmirotta, Guendalina}, year={2026}, pages={456–479} }'
chicago: 'Olbrich, Martin, and Guendalina Palmirotta. “Solvability of Invariant
Systems of Differential Equations on H2$\mathbb {H}^2$ and Beyond.” Mathematische
Nachrichten 299, no. 2 (2026): 456–79. https://doi.org/10.1002/mana.70100.'
ieee: 'M. Olbrich and G. Palmirotta, “Solvability of invariant systems of differential
equations on H2$\mathbb {H}^2$ and beyond,” Mathematische Nachrichten,
vol. 299, no. 2, pp. 456–479, 2026, doi: 10.1002/mana.70100.'
mla: Olbrich, Martin, and Guendalina Palmirotta. “Solvability of Invariant Systems
of Differential Equations on H2$\mathbb {H}^2$ and Beyond.” Mathematische Nachrichten,
vol. 299, no. 2, Wiley, 2026, pp. 456–79, doi:10.1002/mana.70100.
short: M. Olbrich, G. Palmirotta, Mathematische Nachrichten 299 (2026) 456–479.
date_created: 2026-02-20T19:56:33Z
date_updated: 2026-02-20T20:01:56Z
department:
- _id: '548'
doi: 10.1002/mana.70100
intvolume: ' 299'
issue: '2'
language:
- iso: eng
page: 456-479
publication: Mathematische Nachrichten
publication_identifier:
issn:
- 0025-584X
- 1522-2616
publication_status: published
publisher: Wiley
status: public
title: Solvability of invariant systems of differential equations on H2$\mathbb {H}^2$
and beyond
type: journal_article
user_id: '109467'
volume: 299
year: '2026'
...
---
_id: '57580'
abstract:
- lang: eng
text: We investigate dispersive and Strichartz estimates for the Schrödinger equation
involving the fractional Laplacian in real hyperbolic spaces and their discrete
analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates
on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives.
A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears
on homogeneous trees, due to the triviality of the estimates for small times.
author:
- first_name: Guendalina
full_name: Palmirotta, Guendalina
id: '109467'
last_name: Palmirotta
- first_name: Yannick
full_name: Sire, Yannick
last_name: Sire
- first_name: Jean-Philippe
full_name: Anker, Jean-Philippe
last_name: Anker
citation:
ama: Palmirotta G, Sire Y, Anker J-P. The Schrödinger equation with fractional Laplacian
on hyperbolic spaces and homogeneous trees. Journal of Differential Equations.
Published online 2026. doi:10.1016/j.jde.2025.114065
apa: Palmirotta, G., Sire, Y., & Anker, J.-P. (2026). The Schrödinger equation
with fractional Laplacian on hyperbolic spaces and homogeneous trees. Journal
of Differential Equations. https://doi.org/10.1016/j.jde.2025.114065
bibtex: '@article{Palmirotta_Sire_Anker_2026, title={The Schrödinger equation with
fractional Laplacian on hyperbolic spaces and homogeneous trees}, DOI={10.1016/j.jde.2025.114065},
journal={Journal of Differential Equations}, publisher={Elsevier}, author={Palmirotta,
Guendalina and Sire, Yannick and Anker, Jean-Philippe}, year={2026} }'
chicago: Palmirotta, Guendalina, Yannick Sire, and Jean-Philippe Anker. “The Schrödinger
Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.”
Journal of Differential Equations, 2026. https://doi.org/10.1016/j.jde.2025.114065.
ieee: 'G. Palmirotta, Y. Sire, and J.-P. Anker, “The Schrödinger equation with fractional
Laplacian on hyperbolic spaces and homogeneous trees,” Journal of Differential
Equations, 2026, doi: 10.1016/j.jde.2025.114065.'
mla: Palmirotta, Guendalina, et al. “The Schrödinger Equation with Fractional Laplacian
on Hyperbolic Spaces and Homogeneous Trees.” Journal of Differential Equations,
Elsevier, 2026, doi:10.1016/j.jde.2025.114065.
short: G. Palmirotta, Y. Sire, J.-P. Anker, Journal of Differential Equations (2026).
date_created: 2024-12-04T16:21:38Z
date_updated: 2026-03-30T12:03:37Z
department:
- _id: '10'
- _id: '548'
doi: 10.1016/j.jde.2025.114065
external_id:
arxiv:
- '2412.00780'
keyword:
- Schrödinger equation
- Fractional Laplacian
- Dispersive estimates
- Strichartz estimates
- Real hyperbolic spaces
- Homogeneous trees
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.jde.2025.114065
oa: '1'
project:
- _id: '356'
name: 'TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem
Volumen (Teilprojekt B02)'
publication: Journal of Differential Equations
publication_status: published
publisher: Elsevier
related_material:
link:
- relation: confirmation
url: https://www.sciencedirect.com/science/article/pii/S0022039625010927?via%3Dihub
status: public
title: The Schrödinger equation with fractional Laplacian on hyperbolic spaces and
homogeneous trees
type: journal_article
user_id: '109467'
year: '2026'
...
---
_id: '65232'
abstract:
- lang: eng
text: On finite regular graphs, we construct Patterson-Sullivan distributions associated
with eigenfunctions of the discrete Laplace operator via their boundary values
on the phase space. These distributions are closely related to Wigner distributions
defined via a pseudo-differential calculus on graphs, which appear naturally in
the study of quantum chaos. Using a pairing formula, we prove that Patterson-Sullivan
distributions are also related to invariant Ruelle distributions arising from
the transfer operator of the geodesic flow on the shift space. Both relationships
provide discrete analogues of results for compact hyperbolic surfaces obtained
by Anantharaman-Zelditch and by Guillarmou-Hilgert-Weich.
author:
- first_name: Christian
full_name: Arends, Christian
last_name: Arends
- first_name: Guendalina
full_name: Palmirotta, Guendalina
id: '109467'
last_name: Palmirotta
citation:
ama: Arends C, Palmirotta G. Patterson-Sullivan distributions of finite regular
graphs. arXiv:260309779. Published online 2026.
apa: Arends, C., & Palmirotta, G. (2026). Patterson-Sullivan distributions of
finite regular graphs. In arXiv:2603.09779.
bibtex: '@article{Arends_Palmirotta_2026, title={Patterson-Sullivan distributions
of finite regular graphs}, journal={arXiv:2603.09779}, author={Arends, Christian
and Palmirotta, Guendalina}, year={2026} }'
chicago: Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions
of Finite Regular Graphs.” ArXiv:2603.09779, 2026.
ieee: C. Arends and G. Palmirotta, “Patterson-Sullivan distributions of finite regular
graphs,” arXiv:2603.09779. 2026.
mla: Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions
of Finite Regular Graphs.” ArXiv:2603.09779, 2026.
short: C. Arends, G. Palmirotta, ArXiv:2603.09779 (2026).
date_created: 2026-03-30T11:56:04Z
date_updated: 2026-03-30T12:02:56Z
department:
- _id: '548'
- _id: '10'
- _id: '34'
external_id:
arxiv:
- '2603.09779'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2603.09779
oa: '1'
page: '38'
project:
- _id: '358'
name: 'TRR 358; TP B04: Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden'
publication: arXiv:2603.09779
status: public
title: Patterson-Sullivan distributions of finite regular graphs
type: preprint
user_id: '109467'
year: '2026'
...
---
_id: '32099'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Julia
full_name: Budde, Julia
last_name: Budde
citation:
ama: Weich T, Budde J. Wave Front Sets of Nilpotent Lie Group Representations. Journal
of Functional Analysis. 2025;288(1). doi:
https://doi.org/10.1016/j.jfa.2024.110684
apa: Weich, T., & Budde, J. (2025). Wave Front Sets of Nilpotent Lie Group Representations.
Journal of Functional Analysis, 288(1). https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684
bibtex: '@article{Weich_Budde_2025, title={Wave Front Sets of Nilpotent Lie Group
Representations}, volume={288}, DOI={
https://doi.org/10.1016/j.jfa.2024.110684}, number={1}, journal={Journal of
Functional Analysis}, author={Weich, Tobias and Budde, Julia}, year={2025} }'
chicago: Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group
Representations.” Journal of Functional Analysis 288, no. 1 (2025). https://doi.org/
https://doi.org/10.1016/j.jfa.2024.110684.
ieee: 'T. Weich and J. Budde, “Wave Front Sets of Nilpotent Lie Group Representations,”
Journal of Functional Analysis, vol. 288, no. 1, 2025, doi: https://doi.org/10.1016/j.jfa.2024.110684.'
mla: Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.”
Journal of Functional Analysis, vol. 288, no. 1, 2025, doi: https://doi.org/10.1016/j.jfa.2024.110684.
short: T. Weich, J. Budde, Journal of Functional Analysis 288 (2025).
date_created: 2022-06-22T09:56:43Z
date_updated: 2024-09-25T08:18:44Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: ' https://doi.org/10.1016/j.jfa.2024.110684'
file:
- access_level: open_access
content_type: application/pdf
creator: weich
date_created: 2022-06-22T09:56:39Z
date_updated: 2022-06-22T09:56:39Z
file_id: '32100'
file_name: 2103.02968.pdf
file_size: 978990
relation: main_file
file_date_updated: 2022-06-22T09:56:39Z
has_accepted_license: '1'
intvolume: ' 288'
issue: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '356'
grant_number: '491392403'
name: 'TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem
Volumen (Teilprojekt B02)'
- _id: '355'
grant_number: '422642921'
name: Mikrolokale Methoden für hyperbolische Dynamiken
publication: Journal of Functional Analysis
status: public
title: Wave Front Sets of Nilpotent Lie Group Representations
type: journal_article
user_id: '49178'
volume: 288
year: '2025'
...
---
_id: '53414'
abstract:
- lang: eng
text: "By constructing a non-empty domain of discontinuity in a suitable homogeneous\r\nspace,
we prove that every torsion-free projective Anosov subgroup is the\r\nmonodromy
group of a locally homogeneous contact Axiom A dynamical system with\r\na unique
basic hyperbolic set on which the flow is conjugate to the refraction\r\nflow
of Sambarino. Under the assumption of irreducibility, we utilize the work\r\nof
Stoyanov to establish spectral estimates for the associated complex Ruelle\r\ntransfer
operators, and by way of corollary: exponential mixing, exponentially\r\ndecaying
error term in the prime orbit theorem, and a spectral gap for the\r\nRuelle zeta
function. With no irreducibility assumption, results of\r\nDyatlov-Guillarmou
imply the global meromorphic continuation of zeta functions\r\nwith smooth weights,
as well as the existence of a discrete spectrum of\r\nRuelle-Pollicott resonances
and (co)-resonant states. We apply our results to\r\nspace-like geodesic flows
for the convex cocompact pseudo-Riemannian manifolds\r\nof Danciger-Gu\\'eritaud-Kassel,
and the Benoist-Hilbert geodesic flow for\r\nstrictly convex real projective manifolds."
article_type: original
author:
- first_name: Benjamin
full_name: Delarue, Benjamin
id: '70575'
last_name: Delarue
- first_name: Daniel
full_name: Monclair, Daniel
last_name: Monclair
- first_name: Andrew
full_name: Sanders, Andrew
last_name: Sanders
citation:
ama: 'Delarue B, Monclair D, Sanders A. Locally homogeneous Axiom A flows I: projective
Anosov subgroups and exponential mixing. Geometric and Functional Analysis
(GAFA). 2025;35:673–735. doi:10.1007/s00039-025-00712-2'
apa: 'Delarue, B., Monclair, D., & Sanders, A. (2025). Locally homogeneous Axiom
A flows I: projective Anosov subgroups and exponential mixing. Geometric and
Functional Analysis (GAFA), 35, 673–735. https://doi.org/10.1007/s00039-025-00712-2'
bibtex: '@article{Delarue_Monclair_Sanders_2025, title={Locally homogeneous Axiom
A flows I: projective Anosov subgroups and exponential mixing}, volume={35}, DOI={10.1007/s00039-025-00712-2},
journal={Geometric and Functional Analysis (GAFA)}, author={Delarue, Benjamin
and Monclair, Daniel and Sanders, Andrew}, year={2025}, pages={673–735} }'
chicago: 'Delarue, Benjamin, Daniel Monclair, and Andrew Sanders. “Locally Homogeneous
Axiom A Flows I: Projective Anosov Subgroups and Exponential Mixing.” Geometric
and Functional Analysis (GAFA) 35 (2025): 673–735. https://doi.org/10.1007/s00039-025-00712-2.'
ieee: 'B. Delarue, D. Monclair, and A. Sanders, “Locally homogeneous Axiom A flows
I: projective Anosov subgroups and exponential mixing,” Geometric and Functional
Analysis (GAFA), vol. 35, pp. 673–735, 2025, doi: 10.1007/s00039-025-00712-2.'
mla: 'Delarue, Benjamin, et al. “Locally Homogeneous Axiom A Flows I: Projective
Anosov Subgroups and Exponential Mixing.” Geometric and Functional Analysis
(GAFA), vol. 35, 2025, pp. 673–735, doi:10.1007/s00039-025-00712-2.'
short: B. Delarue, D. Monclair, A. Sanders, Geometric and Functional Analysis (GAFA)
35 (2025) 673–735.
date_created: 2024-04-11T12:31:34Z
date_updated: 2026-01-09T09:25:45Z
department:
- _id: '548'
doi: 10.1007/s00039-025-00712-2
intvolume: ' 35'
language:
- iso: eng
page: 673–735
publication: Geometric and Functional Analysis (GAFA)
publication_status: published
status: public
title: 'Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential
mixing'
type: journal_article
user_id: '70575'
volume: 35
year: '2025'
...
---
_id: '53412'
abstract:
- lang: eng
text: "Let $M$ be a symplectic manifold carrying a Hamiltonian $S^1$-action with\r\nmomentum
map $J:M \\rightarrow \\mathbb{R}$ and consider the corresponding\r\nsymplectic
quotient $\\mathcal{M}_0:=J^{-1}(0)/S^1$. We extend Sjamaar's complex\r\nof differential
forms on $\\mathcal{M}_0$, whose cohomology is isomorphic to the\r\nsingular cohomology
$H(\\mathcal{M}_0;\\mathbb{R})$ of $\\mathcal{M}_0$ with real\r\ncoefficients,
to a complex of differential forms on $\\mathcal{M}_0$ associated\r\nwith a partial
desingularization $\\widetilde{\\mathcal{M}}_0$, which we call\r\nresolution differential
forms. The cohomology of that complex turns out to be\r\nisomorphic to the de
Rham cohomology $H(\\widetilde{ \\mathcal{M}}_0)$ of\r\n$\\widetilde{\\mathcal{M}}_0$.
Based on this, we derive a long exact sequence\r\ninvolving both $H(\\mathcal{M}_0;\\mathbb{R})$
and $H(\\widetilde{\r\n\\mathcal{M}}_0)$ and give conditions for its splitting.
We then define a Kirwan\r\nmap $\\mathcal{K}:H_{S^1}(M) \\rightarrow H(\\widetilde{\\mathcal{M}}_0)$
from the\r\nequivariant cohomology $H_{S^1}(M)$ of $M$ to $H(\\widetilde{\\mathcal{M}}_0)$\r\nand
show that its image contains the image of $H(\\mathcal{M}_0;\\mathbb{R})$ in\r\n$H(\\widetilde{\\mathcal{M}}_0)$
under the natural inclusion. Combining both\r\nresults in the case that all fixed
point components of $M$ have vanishing odd\r\ncohomology we obtain a surjection
$\\check \\kappa:H^\\textrm{ev}_{S^1}(M)\r\n\\rightarrow H^\\textrm{ev}(\\mathcal{M}_0;\\mathbb{R})$
in even degrees, while\r\nalready simple examples show that a similar surjection
in odd degrees does not\r\nexist in general. As an interesting class of examples
we study abelian polygon\r\nspaces."
article_type: original
author:
- first_name: Benjamin
full_name: Delarue, Benjamin
id: '70575'
last_name: Delarue
- first_name: Pablo
full_name: Ramacher, Pablo
last_name: Ramacher
- first_name: Maximilian
full_name: Schmitt, Maximilian
last_name: Schmitt
citation:
ama: Delarue B, Ramacher P, Schmitt M. Singular cohomology of symplectic quotients
by circle actions and Kirwan surjectivity. Transformation Groups. Published
online 2025. doi:10.1007/s00031-025-09924-0
apa: Delarue, B., Ramacher, P., & Schmitt, M. (2025). Singular cohomology of
symplectic quotients by circle actions and Kirwan surjectivity. Transformation
Groups. https://doi.org/10.1007/s00031-025-09924-0
bibtex: '@article{Delarue_Ramacher_Schmitt_2025, title={Singular cohomology of symplectic
quotients by circle actions and Kirwan surjectivity}, DOI={10.1007/s00031-025-09924-0},
journal={Transformation Groups}, author={Delarue, Benjamin and Ramacher, Pablo
and Schmitt, Maximilian}, year={2025} }'
chicago: Delarue, Benjamin, Pablo Ramacher, and Maximilian Schmitt. “Singular Cohomology
of Symplectic Quotients by Circle Actions and Kirwan Surjectivity.” Transformation
Groups, 2025. https://doi.org/10.1007/s00031-025-09924-0.
ieee: 'B. Delarue, P. Ramacher, and M. Schmitt, “Singular cohomology of symplectic
quotients by circle actions and Kirwan surjectivity,” Transformation Groups,
2025, doi: 10.1007/s00031-025-09924-0.'
mla: Delarue, Benjamin, et al. “Singular Cohomology of Symplectic Quotients by Circle
Actions and Kirwan Surjectivity.” Transformation Groups, 2025, doi:10.1007/s00031-025-09924-0.
short: B. Delarue, P. Ramacher, M. Schmitt, Transformation Groups (2025).
date_created: 2024-04-11T12:30:59Z
date_updated: 2026-01-09T09:27:08Z
department:
- _id: '548'
doi: 10.1007/s00031-025-09924-0
language:
- iso: eng
publication: Transformation Groups
publication_status: epub_ahead
status: public
title: Singular cohomology of symplectic quotients by circle actions and Kirwan surjectivity
type: journal_article
user_id: '70575'
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. Journal of Lie Theory. 35((4)):787--804.
apa: Delarue, B., & Hilgert, J. (n.d.). Quantum resonances and scattering poles
of classical rank one locally symmetric spaces. Journal of Lie Theory,
35((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.” Journal of Lie Theory
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,” Journal of Lie Theory, 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.” Journal of Lie Theory,
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: '51207'
abstract:
- lang: eng
text: "Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact
type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We
show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic
growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain
that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$."
article_number: '76'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
orcid: 0000-0001-8893-2045
citation:
ama: 'Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case.
Geom Dedicata. 2024;218. doi:https://doi.org/10.1007/s10711-024-00904-4'
apa: 'Weich, T., & Wolf, L. L. (2024). Temperedness of locally symmetric spaces:
The product case. Geom Dedicata, 218, Article 76. https://doi.org/10.1007/s10711-024-00904-4'
bibtex: '@article{Weich_Wolf_2024, title={Temperedness of locally symmetric spaces:
The product case}, volume={218}, DOI={https://doi.org/10.1007/s10711-024-00904-4},
number={76}, journal={Geom Dedicata}, author={Weich, Tobias and Wolf, Lasse Lennart},
year={2024} }'
chicago: 'Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric
Spaces: The Product Case.” Geom Dedicata 218 (2024). https://doi.org/10.1007/s10711-024-00904-4.'
ieee: 'T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product
case,” Geom Dedicata, vol. 218, Art. no. 76, 2024, doi: https://doi.org/10.1007/s10711-024-00904-4.'
mla: 'Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric
Spaces: The Product Case.” Geom Dedicata, vol. 218, 76, 2024, doi:https://doi.org/10.1007/s10711-024-00904-4.'
short: T. Weich, L.L. Wolf, Geom Dedicata 218 (2024).
date_created: 2024-02-06T21:00:55Z
date_updated: 2024-05-07T11:44:34Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: https://doi.org/10.1007/s10711-024-00904-4
external_id:
arxiv:
- '2304.09573'
intvolume: ' 218'
language:
- iso: eng
publication: Geom Dedicata
status: public
title: 'Temperedness of locally symmetric spaces: The product case'
type: journal_article
user_id: '45027'
volume: 218
year: '2024'
...
---
_id: '55193'
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Hoffmann M, Hilgert J, Weich T. Ebene euklidische Geometrie. Algebraisierung,
Axiomatisierung und Schnittstellen zur Schulmathematik. Springer Berlin Heidelberg;
2024. doi:10.1007/978-3-662-67357-7
apa: Hoffmann, M., Hilgert, J., & Weich, T. (2024). Ebene euklidische Geometrie.
Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik. Springer
Berlin Heidelberg. https://doi.org/10.1007/978-3-662-67357-7
bibtex: '@book{Hoffmann_Hilgert_Weich_2024, place={Berlin, Heidelberg}, title={Ebene
euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur
Schulmathematik}, DOI={10.1007/978-3-662-67357-7},
publisher={Springer Berlin Heidelberg}, author={Hoffmann, Max and Hilgert, Joachim
and Weich, Tobias}, year={2024} }'
chicago: 'Hoffmann, Max, Joachim Hilgert, and Tobias Weich. Ebene euklidische
Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik.
Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. https://doi.org/10.1007/978-3-662-67357-7.'
ieee: 'M. Hoffmann, J. Hilgert, and T. Weich, Ebene euklidische Geometrie. Algebraisierung,
Axiomatisierung und Schnittstellen zur Schulmathematik. Berlin, Heidelberg:
Springer Berlin Heidelberg, 2024.'
mla: Hoffmann, Max, et al. Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung
und Schnittstellen zur Schulmathematik. Springer Berlin Heidelberg, 2024,
doi:10.1007/978-3-662-67357-7.
short: M. Hoffmann, J. Hilgert, T. Weich, Ebene euklidische Geometrie. Algebraisierung,
Axiomatisierung und Schnittstellen zur Schulmathematik, Springer Berlin Heidelberg,
Berlin, Heidelberg, 2024.
date_created: 2024-07-12T08:36:42Z
date_updated: 2024-08-08T08:05:30Z
department:
- _id: '97'
- _id: '643'
- _id: '548'
doi: 10.1007/978-3-662-67357-7
language:
- iso: ger
place: Berlin, Heidelberg
publication_identifier:
isbn:
- '9783662673560'
- '9783662673577'
publication_status: published
publisher: Springer Berlin Heidelberg
status: public
title: Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen
zur Schulmathematik
type: book
user_id: '220'
year: '2024'
...
---
_id: '32101'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Yannick
full_name: Guedes Bonthonneau, Yannick
last_name: Guedes Bonthonneau
- first_name: Colin
full_name: Guillarmou, Colin
last_name: Guillarmou
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonances
of Anosov actions. J Europ Math Soc. 2024;27(8):3085–3147. doi:https://doi.org/10.4171/JEMS/1428
apa: Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., & Hilgert, J. (2024).
Ruelle-Taylor resonances of Anosov actions. J. Europ. Math. Soc., 27(8),
3085–3147. https://doi.org/10.4171/JEMS/1428
bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor
resonances of Anosov actions}, volume={27}, DOI={https://doi.org/10.4171/JEMS/1428},
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.” J. Europ. Math. Soc.
27, no. 8 (2024): 3085–3147. https://doi.org/10.4171/JEMS/1428.'
ieee: 'T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor
resonances of Anosov actions,” J. Europ. Math. Soc., vol. 27, no. 8, pp.
3085–3147, 2024, doi: https://doi.org/10.4171/JEMS/1428.'
mla: Weich, Tobias, et al. “Ruelle-Taylor Resonances of Anosov Actions.” J. Europ.
Math. Soc., vol. 27, no. 8, 2024, pp. 3085–3147, doi:https://doi.org/10.4171/JEMS/1428.
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: '57582'
abstract:
- lang: eng
text: "We prove that the Patterson-Sullivan and Wigner distributions on the unit\r\nsphere
bundle of a convex-cocompact hyperbolic surface are asymptotically\r\nidentical.
This generalizes results in the compact case by\r\nAnantharaman-Zelditch and Hansen-Hilgert-Schr\\\"oder."
author:
- first_name: Benjamin
full_name: Delarue, Benjamin
last_name: Delarue
- first_name: Guendalina
full_name: Palmirotta, Guendalina
last_name: Palmirotta
citation:
ama: Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact
hyperbolic surfaces. arXiv:241119782. Published online 2024.
apa: Delarue, B., & Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions
of convex-cocompact hyperbolic surfaces. In arXiv:2411.19782.
bibtex: '@article{Delarue_Palmirotta_2024, title={Patterson-Sullivan and Wigner
distributions of convex-cocompact hyperbolic surfaces}, journal={arXiv:2411.19782},
author={Delarue, Benjamin and Palmirotta, Guendalina}, year={2024} }'
chicago: Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner
Distributions of Convex-Cocompact Hyperbolic Surfaces.” ArXiv:2411.19782,
2024.
ieee: B. Delarue and G. Palmirotta, “Patterson-Sullivan and Wigner distributions
of convex-cocompact hyperbolic surfaces,” arXiv:2411.19782. 2024.
mla: Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner
Distributions of Convex-Cocompact Hyperbolic Surfaces.” ArXiv:2411.19782,
2024.
short: B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).
date_created: 2024-12-04T16:28:05Z
date_updated: 2024-12-04T16:33:27Z
department:
- _id: '10'
- _id: '548'
external_id:
arxiv:
- '2411.19782'
language:
- iso: eng
project:
- _id: '356'
grant_number: '491392403'
name: 'TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem
Volumen (Teilprojekt B02)'
publication: arXiv:2411.19782
status: public
title: Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic
surfaces
type: preprint
user_id: '109467'
year: '2024'
...
---
_id: '32097'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Yannick
full_name: Guedes Bonthonneau, Yannick
last_name: Guedes Bonthonneau
- first_name: Colin
full_name: Guillarmou, Colin
last_name: Guillarmou
citation:
ama: 'Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions.
Journal of Differential Geometry. 2024;128:959-1026. doi: DOI: 10.4310/jdg/1729092452'
apa: 'Weich, T., Guedes Bonthonneau, Y., & Guillarmou, C. (2024). SRB Measures
of Anosov Actions. Journal of Differential Geometry, 128, 959–1026.
https://doi.org/ DOI: 10.4310/jdg/1729092452'
bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures
of Anosov Actions}, volume={128}, DOI={
DOI: 10.4310/jdg/1729092452}, journal={Journal of Differential Geometry},
author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin},
year={2024}, pages={959–1026} }'
chicago: 'Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB
Measures of Anosov Actions.” Journal of Differential Geometry 128 (2024):
959–1026. https://doi.org/
DOI: 10.4310/jdg/1729092452.'
ieee: 'T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov
Actions,” Journal of Differential Geometry, vol. 128, pp. 959–1026, 2024,
doi: DOI: 10.4310/jdg/1729092452.'
mla: 'Weich, Tobias, et al. “SRB Measures of Anosov Actions.” Journal of Differential
Geometry, vol. 128, 2024, pp. 959–1026, doi: DOI: 10.4310/jdg/1729092452.'
short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry
128 (2024) 959–1026.
date_created: 2022-06-22T09:56:23Z
date_updated: 2025-01-02T15:39:43Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: ' DOI: 10.4310/jdg/1729092452'
external_id:
arxiv:
- https://arxiv.org/abs/2103.12127
file:
- access_level: open_access
content_type: application/pdf
creator: weich
date_created: 2022-06-22T09:56:08Z
date_updated: 2022-06-22T09:56:08Z
file_id: '32098'
file_name: 2103.12127.pdf
file_size: 745870
relation: main_file
file_date_updated: 2022-06-22T09:56:08Z
has_accepted_license: '1'
intvolume: ' 128'
language:
- iso: eng
oa: '1'
page: 959-1026
project:
- _id: '358'
grant_number: '491392403'
name: TRR 358 - Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden (Teilprojekt
B04)
- _id: '355'
grant_number: '422642921'
name: Mikrolokale Methoden für hyperbolische Dynamiken
publication: Journal of Differential Geometry
status: public
title: SRB Measures of Anosov Actions
type: journal_article
user_id: '49178'
volume: 128
year: '2024'
...
---
_id: '58873'
abstract:
- lang: eng
text: "We prove that the Patterson-Sullivan and Wigner distributions on the unit\r\nsphere
bundle of a convex-cocompact hyperbolic surface are asymptotically\r\nidentical.
This generalizes results in the compact case by\r\nAnantharaman-Zelditch and Hansen-Hilgert-Schr\\\"oder."
author:
- first_name: Benjamin
full_name: Delarue, Benjamin
id: '70575'
last_name: Delarue
- first_name: Guendalina
full_name: Palmirotta, Guendalina
id: '109467'
last_name: Palmirotta
citation:
ama: Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact
hyperbolic surfaces. arXiv:241119782. Published online 2024.
apa: Delarue, B., & Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions
of convex-cocompact hyperbolic surfaces. In arXiv:2411.19782.
bibtex: '@article{Delarue_Palmirotta_2024, title={Patterson-Sullivan and Wigner
distributions of convex-cocompact hyperbolic surfaces}, journal={arXiv:2411.19782},
author={Delarue, Benjamin and Palmirotta, Guendalina}, year={2024} }'
chicago: Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner
Distributions of Convex-Cocompact Hyperbolic Surfaces.” ArXiv:2411.19782,
2024.
ieee: B. Delarue and G. Palmirotta, “Patterson-Sullivan and Wigner distributions
of convex-cocompact hyperbolic surfaces,” arXiv:2411.19782. 2024.
mla: Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner
Distributions of Convex-Cocompact Hyperbolic Surfaces.” ArXiv:2411.19782,
2024.
short: B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).
date_created: 2025-02-28T10:32:30Z
date_updated: 2026-03-30T12:01:12Z
department:
- _id: '548'
external_id:
arxiv:
- '2411.19782'
language:
- iso: eng
project:
- _id: '356'
name: 'TRR 358; TP B02: Spektraltheorie in höherem Rang und unendlichem Volumen'
publication: arXiv:2411.19782
status: public
title: Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic
surfaces
type: preprint
user_id: '109467'
year: '2024'
...
---
_id: '31189'
abstract:
- lang: eng
text: "Given a geometrically finite hyperbolic surface of infinite volume it is
a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator
has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization
of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential
operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of
higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe
geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding
principal eigenvalues. A large class of examples fulfilling these\r\nassumptions
are the non-compact quotients by Anosov subgroups."
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
citation:
ama: Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally
symmetric spaces. Communications in Mathematical Physics. 2023;403. doi:https://doi.org/10.1007/s00220-023-04819-1
apa: Weich, T., & Wolf, L. L. (2023). Absence of principal eigenvalues for higher
rank locally symmetric spaces. Communications in Mathematical Physics,
403. https://doi.org/10.1007/s00220-023-04819-1
bibtex: '@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher
rank locally symmetric spaces}, volume={403}, DOI={https://doi.org/10.1007/s00220-023-04819-1},
journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf,
Lasse Lennart}, year={2023} }'
chicago: Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues
for Higher Rank Locally Symmetric Spaces.” Communications in Mathematical
Physics 403 (2023). https://doi.org/10.1007/s00220-023-04819-1.
ieee: 'T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank
locally symmetric spaces,” Communications in Mathematical Physics, vol.
403, 2023, doi: https://doi.org/10.1007/s00220-023-04819-1.'
mla: Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for
Higher Rank Locally Symmetric Spaces.” Communications in Mathematical Physics,
vol. 403, 2023, doi:https://doi.org/10.1007/s00220-023-04819-1.
short: T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).
date_created: 2022-05-11T10:38:11Z
date_updated: 2024-02-06T20:52:40Z
department:
- _id: '10'
- _id: '548'
- _id: '623'
doi: https://doi.org/10.1007/s00220-023-04819-1
external_id:
arxiv:
- '2205.03167'
intvolume: ' 403'
language:
- iso: eng
publication: Communications in Mathematical Physics
publication_identifier:
unknown:
- 1275-1295
status: public
title: Absence of principal eigenvalues for higher rank locally symmetric spaces
type: journal_article
user_id: '49178'
volume: 403
year: '2023'
...
---
_id: '51206'
abstract:
- lang: eng
text: "We present a numerical algorithm for the computation of invariant Ruelle\r\ndistributions
on convex co-compact hyperbolic surfaces. This is achieved by\r\nexploiting the
connection between invariant Ruelle distributions and residues\r\nof meromorphically
continued weighted zeta functions established by the authors\r\ntogether with
Barkhofen (2021). To make this applicable for numerics we express\r\nthe weighted
zeta as the logarithmic derivative of a suitable parameter\r\ndependent Fredholm
determinant similar to Borthwick (2014). As an additional\r\ndifficulty our transfer
operator has to include a contracting direction which\r\nwe account for with techniques
developed by Rugh (1992). We achieve a further\r\nimprovement in convergence speed
for our algorithm in the case of surfaces with\r\nadditional symmetries by proving
and applying a symmetry reduction of weighted\r\nzeta functions."
author:
- first_name: Philipp
full_name: Schütte, Philipp
id: '50168'
last_name: Schütte
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Schütte P, Weich T. Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic
Surfaces -- A Numerical Algorithm via Weighted Zeta Functions. arXiv:230813463.
Published online 2023.
apa: Schütte, P., & Weich, T. (2023). Invariant Ruelle Distributions on Convex-Cocompact
Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions. In
arXiv:2308.13463.
bibtex: '@article{Schütte_Weich_2023, title={Invariant Ruelle Distributions on Convex-Cocompact
Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions}, journal={arXiv:2308.13463},
author={Schütte, Philipp and Weich, Tobias}, year={2023} }'
chicago: Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on
Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta
Functions.” ArXiv:2308.13463, 2023.
ieee: P. Schütte and T. Weich, “Invariant Ruelle Distributions on Convex-Cocompact
Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions,” arXiv:2308.13463.
2023.
mla: Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact
Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions.” ArXiv:2308.13463,
2023.
short: P. Schütte, T. Weich, ArXiv:2308.13463 (2023).
date_created: 2024-02-06T20:58:35Z
date_updated: 2024-02-11T19:56:01Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
arxiv:
- '2308.13463'
language:
- iso: eng
publication: arXiv:2308.13463
status: public
title: Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces --
A Numerical Algorithm via Weighted Zeta Functions
type: preprint
user_id: '49178'
year: '2023'
...
---
_id: '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. Journal de l’École polytechnique
— Mathématiques. 2023;10:335-403. doi:10.5802/jep.220'
apa: 'Arends, C., & Hilgert, J. (2023). Spectral correspondences for rank one
locally symmetric spaces: the case of exceptional parameters. Journal de l’École
Polytechnique — Mathématiques, 10, 335–403. https://doi.org/10.5802/jep.220'
bibtex: '@article{Arends_Hilgert_2023, title={Spectral correspondences for rank
one locally symmetric spaces: the case of exceptional parameters}, volume={10},
DOI={10.5802/jep.220}, 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.” Journal
de l’École Polytechnique — Mathématiques 10 (2023): 335–403. https://doi.org/10.5802/jep.220.'
ieee: 'C. Arends and J. Hilgert, “Spectral correspondences for rank one locally
symmetric spaces: the case of exceptional parameters,” Journal de l’École polytechnique
— Mathématiques, vol. 10, pp. 335–403, 2023, doi: 10.5802/jep.220.'
mla: 'Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank
One Locally Symmetric Spaces: The Case of Exceptional Parameters.” Journal
de l’École Polytechnique — Mathématiques, vol. 10, 2023, pp. 335–403, doi:10.5802/jep.220.'
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: '53404'
abstract:
- lang: eng
text: "In this short note we observe, on locally symmetric spaces of higher rank,
a\r\nconnection between the growth indicator function introduced by Quint and
the\r\nmodified critical exponent of the Poincar\\'e series equipped with the\r\npolyhedral
distance. As a consequence, we provide a different characterization\r\nof the
bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms\r\nof the
growth indicator function. Moreover, we explore the relationship between\r\nthese
three objects and the temperedness."
author:
- first_name: Lasse L.
full_name: Wolf, Lasse L.
last_name: Wolf
- first_name: Hong-Wei
full_name: Zhang, Hong-Wei
last_name: Zhang
citation:
ama: Wolf LL, Zhang H-W. $L^2$-spectrum, growth indicator function and critical
exponent on locally symmetric spaces. arXiv:231111770. Published online
2023.
apa: Wolf, L. L., & Zhang, H.-W. (2023). $L^2$-spectrum, growth indicator function
and critical exponent on locally symmetric spaces. In arXiv:2311.11770.
bibtex: '@article{Wolf_Zhang_2023, title={$L^2$-spectrum, growth indicator function
and critical exponent on locally symmetric spaces}, journal={arXiv:2311.11770},
author={Wolf, Lasse L. and Zhang, Hong-Wei}, year={2023} }'
chicago: Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function
and Critical Exponent on Locally Symmetric Spaces.” ArXiv:2311.11770,
2023.
ieee: L. L. Wolf and H.-W. Zhang, “$L^2$-spectrum, growth indicator function and
critical exponent on locally symmetric spaces,” arXiv:2311.11770. 2023.
mla: Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function
and Critical Exponent on Locally Symmetric Spaces.” ArXiv:2311.11770,
2023.
short: L.L. Wolf, H.-W. Zhang, ArXiv:2311.11770 (2023).
date_created: 2024-04-10T13:45:59Z
date_updated: 2024-04-10T13:48:17Z
department:
- _id: '10'
- _id: '548'
external_id:
arxiv:
- '2311.11770'
language:
- iso: eng
publication: arXiv:2311.11770
status: public
title: $L^2$-spectrum, growth indicator function and critical exponent on locally
symmetric spaces
type: preprint
user_id: '45027'
year: '2023'
...
---
_id: '53410'
abstract:
- lang: eng
text: AbstractWe consider a geodesic billiard system
consisting of a complete Riemannian manifold and an obstacle submanifold with
boundary at which the trajectories of the geodesic flow experience specular reflections.
We show that if the geodesic billiard system is hyperbolic on its trapped set
and the latter is compact and non-grazing, the techniques for open hyperbolic
systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146,
2016) can be applied to a smooth model for the discontinuous flow defined by the
non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent
for the generator of the billiard flow. As an application we prove a meromorphic
continuation of weighted zeta functions together with explicit residue formulae.
In particular, our results apply to scattering by convex obstacles in the Euclidean
plane.
author:
- first_name: Benjamin
full_name: Delarue, Benjamin
id: '70575'
last_name: Delarue
- first_name: Philipp
full_name: Schütte, Philipp
id: '50168'
last_name: Schütte
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle
Scattering via Smooth Models. Annales Henri Poincaré. 2023;25(2):1607-1656.
doi:10.1007/s00023-023-01379-x
apa: Delarue, B., Schütte, P., & Weich, T. (2023). Resonances and Weighted Zeta
Functions for Obstacle Scattering via Smooth Models. Annales Henri Poincaré,
25(2), 1607–1656. https://doi.org/10.1007/s00023-023-01379-x
bibtex: '@article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta
Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={10.1007/s00023-023-01379-x},
number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and
Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich,
Tobias}, year={2023}, pages={1607–1656} }'
chicago: 'Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and
Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” Annales
Henri Poincaré 25, no. 2 (2023): 1607–56. https://doi.org/10.1007/s00023-023-01379-x.'
ieee: 'B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions
for Obstacle Scattering via Smooth Models,” Annales Henri Poincaré, vol.
25, no. 2, pp. 1607–1656, 2023, doi: 10.1007/s00023-023-01379-x.'
mla: Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle
Scattering via Smooth Models.” Annales Henri Poincaré, vol. 25, no. 2,
Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:10.1007/s00023-023-01379-x.
short: B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.
date_created: 2024-04-11T12:30:14Z
date_updated: 2024-04-11T12:37:34Z
department:
- _id: '548'
doi: 10.1007/s00023-023-01379-x
intvolume: ' 25'
issue: '2'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 1607-1656
publication: Annales Henri Poincaré
publication_identifier:
issn:
- 1424-0637
- 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models
type: journal_article
user_id: '70575'
volume: 25
year: '2023'
...
---
_id: '53411'
abstract:
- lang: eng
text: "We compute a Riemann-Roch formula for the invariant Riemann-Roch number of
a\r\nquantizable Hamiltonian $S^1$-manifold $(M,\\omega,\\mathcal{J})$ in terms
of the\r\ngeometry of its symplectic quotient, allowing $0$ to be a singular value
of the\r\nmoment map $\\mathcal{J}:M\\to\\mathbb{R}$. The formula involves a new
explicit\r\nlocal invariant of the singularities. Our approach relies on a complete\r\nsingular
stationary phase expansion of the associated Witten integral."
author:
- first_name: Benjamin
full_name: Delarue, Benjamin
id: '70575'
last_name: Delarue
- first_name: Louis
full_name: Ioos, Louis
last_name: Ioos
- first_name: Pablo
full_name: Ramacher, Pablo
last_name: Ramacher
citation:
ama: Delarue B, Ioos L, Ramacher P. A Riemann-Roch formula for singular reductions
by circle actions. arXiv:230209894. Published online 2023.
apa: Delarue, B., Ioos, L., & Ramacher, P. (2023). A Riemann-Roch formula for
singular reductions by circle actions. In arXiv:2302.09894.
bibtex: '@article{Delarue_Ioos_Ramacher_2023, title={A Riemann-Roch formula for
singular reductions by circle actions}, journal={arXiv:2302.09894}, author={Delarue,
Benjamin and Ioos, Louis and Ramacher, Pablo}, year={2023} }'
chicago: Delarue, Benjamin, Louis Ioos, and Pablo Ramacher. “A Riemann-Roch Formula
for Singular Reductions by Circle Actions.” ArXiv:2302.09894, 2023.
ieee: B. Delarue, L. Ioos, and P. Ramacher, “A Riemann-Roch formula for singular
reductions by circle actions,” arXiv:2302.09894. 2023.
mla: Delarue, Benjamin, et al. “A Riemann-Roch Formula for Singular Reductions by
Circle Actions.” ArXiv:2302.09894, 2023.
short: B. Delarue, L. Ioos, P. Ramacher, ArXiv:2302.09894 (2023).
date_created: 2024-04-11T12:30:42Z
date_updated: 2024-04-11T12:37:09Z
department:
- _id: '548'
external_id:
arxiv:
- '2302.09894'
language:
- iso: eng
publication: arXiv:2302.09894
status: public
title: A Riemann-Roch formula for singular reductions by circle actions
type: preprint
user_id: '70575'
year: '2023'
...