---
_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: '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: '64570'
article_number: '9'
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. Delorme’s intertwining conditions for sections of
homogeneous vector bundles on two- and three-dimensional hyperbolic spaces. Annals
of Global Analysis and Geometry. 2022;63(1). doi:10.1007/s10455-022-09882-w
apa: Olbrich, M., & Palmirotta, G. (2022). Delorme’s intertwining conditions
for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic
spaces. Annals of Global Analysis and Geometry, 63(1), Article 9.
https://doi.org/10.1007/s10455-022-09882-w
bibtex: '@article{Olbrich_Palmirotta_2022, title={Delorme’s intertwining conditions
for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic
spaces}, volume={63}, DOI={10.1007/s10455-022-09882-w},
number={19}, journal={Annals of Global Analysis and Geometry}, publisher={Springer
Science and Business Media LLC}, author={Olbrich, Martin and Palmirotta, Guendalina},
year={2022} }'
chicago: Olbrich, Martin, and Guendalina Palmirotta. “Delorme’s Intertwining Conditions
for Sections of Homogeneous Vector Bundles on Two- and Three-Dimensional Hyperbolic
Spaces.” Annals of Global Analysis and Geometry 63, no. 1 (2022). https://doi.org/10.1007/s10455-022-09882-w.
ieee: 'M. Olbrich and G. Palmirotta, “Delorme’s intertwining conditions for sections
of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces,”
Annals of Global Analysis and Geometry, vol. 63, no. 1, Art. no. 9, 2022,
doi: 10.1007/s10455-022-09882-w.'
mla: Olbrich, Martin, and Guendalina Palmirotta. “Delorme’s Intertwining Conditions
for Sections of Homogeneous Vector Bundles on Two- and Three-Dimensional Hyperbolic
Spaces.” Annals of Global Analysis and Geometry, vol. 63, no. 1, 9, Springer
Science and Business Media LLC, 2022, doi:10.1007/s10455-022-09882-w.
short: M. Olbrich, G. Palmirotta, Annals of Global Analysis and Geometry 63 (2022).
date_created: 2026-02-20T20:02:50Z
date_updated: 2026-02-20T20:03:38Z
department:
- _id: '10'
- _id: '548'
doi: 10.1007/s10455-022-09882-w
extern: '1'
intvolume: ' 63'
issue: '1'
language:
- iso: eng
publication: Annals of Global Analysis and Geometry
publication_identifier:
issn:
- 0232-704X
- 1572-9060
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Delorme’s intertwining conditions for sections of homogeneous vector bundles
on two- and three-dimensional hyperbolic spaces
type: journal_article
user_id: '109467'
volume: 63
year: '2022'
...
---
_id: '64571'
abstract:
- lang: eng
text: We study the Fourier transform for compactly supported distributional sections
of complex homogeneous vector bundles on symmetric spaces of non-compact type
$X = G/K$. We prove a characterisation of their range. In fact, from Delorme's
Paley-Wiener theorem for compactly supported smooth functions on a real reductive
group of Harish-Chandra class, we deduce topological Paley-Wiener and Paley-Wiener-Schwartz
theorems for sections.
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. A topological Paley-Wiener-Schwartz Theorem for sections
of homogeneous vector bundles on $G/K$. Journal of Lie theory. 2022;34(2):53--384.
apa: Olbrich, M., & Palmirotta, G. (2022). A topological Paley-Wiener-Schwartz
Theorem for sections of homogeneous vector bundles on $G/K$. Journal of Lie
Theory, 34(2), 53--384.
bibtex: '@article{Olbrich_Palmirotta_2022, title={A topological Paley-Wiener-Schwartz
Theorem for sections of homogeneous vector bundles on $G/K$}, volume={34}, number={2},
journal={Journal of Lie theory}, publisher={Heldermann Verlag}, author={Olbrich,
Martin and Palmirotta, Guendalina}, year={2022}, pages={53--384} }'
chicago: 'Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz
Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” Journal of Lie
Theory 34, no. 2 (2022): 53--384.'
ieee: M. Olbrich and G. Palmirotta, “A topological Paley-Wiener-Schwartz Theorem
for sections of homogeneous vector bundles on $G/K$,” Journal of Lie theory,
vol. 34, no. 2, pp. 53--384, 2022.
mla: Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz
Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” Journal of Lie
Theory, vol. 34, no. 2, Heldermann Verlag, 2022, pp. 53--384.
short: M. Olbrich, G. Palmirotta, Journal of Lie Theory 34 (2022) 53--384.
date_created: 2026-02-20T20:04:49Z
date_updated: 2026-02-20T20:07:31Z
department:
- _id: '10'
- _id: '548'
extern: '1'
external_id:
arxiv:
- '2202.06905'
intvolume: ' 34'
issue: '2'
language:
- iso: eng
page: 53--384
publication: Journal of Lie theory
publication_status: published
publisher: Heldermann Verlag
status: public
title: A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector
bundles on $G/K$
type: journal_article
user_id: '109467'
volume: 34
year: '2022'
...