---
_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: '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: '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: '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'
...