Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.14426 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909411066249216 |
|---|---|
| author | Delarue, Benjamin Hilgert, Joachim |
| author_facet | Delarue, Benjamin Hilgert, Joachim |
| contents | For negatively curved symmetric spaces it is known from [Hansen-Hilgert-Parthasarathy,2019] that the poles of the scattering matrices defined via the standard intertwining operators for the spherical principal representations of the isometry group are either given as poles of the intertwining operators or as quantum resonances, i.e. poles of the meromorphically continued resolvents of the Laplace-Beltrami operator. We extend this result to classical locally symmetric spaces of negative curvature with convex-cocompact fundamental group using results of Bunke and Olbrich. The method of proof forces us to exclude the spectral parameters corresponding to singular Poisson transforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum resonances and scattering poles of classical rank one locally symmetric spaces Delarue, Benjamin Hilgert, Joachim Spectral Theory Mathematical Physics Group Theory 53C35, 58J50, 81U24, 22E46 For negatively curved symmetric spaces it is known from [Hansen-Hilgert-Parthasarathy,2019] that the poles of the scattering matrices defined via the standard intertwining operators for the spherical principal representations of the isometry group are either given as poles of the intertwining operators or as quantum resonances, i.e. poles of the meromorphically continued resolvents of the Laplace-Beltrami operator. We extend this result to classical locally symmetric spaces of negative curvature with convex-cocompact fundamental group using results of Bunke and Olbrich. The method of proof forces us to exclude the spectral parameters corresponding to singular Poisson transforms. |
| title | Quantum resonances and scattering poles of classical rank one locally symmetric spaces |
| topic | Spectral Theory Mathematical Physics Group Theory 53C35, 58J50, 81U24, 22E46 |
| url | https://arxiv.org/abs/2403.14426 |