Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.11770 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916449113604096 |
|---|---|
| author | Wolf, Lasse L. Zhang, Hong-Wei |
| author_facet | Wolf, Lasse L. Zhang, Hong-Wei |
| contents | In this short note we observe, on locally symmetric spaces of higher rank, a connection between the growth indicator function introduced by Quint and the modified critical exponent of the Poincaré series equipped with the polyhedral distance. As a consequence, we provide a different characterization of the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms of the growth indicator function. Moreover, we explore the relationship between these three objects and the temperedness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11770 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces Wolf, Lasse L. Zhang, Hong-Wei Spectral Theory 22E40, A7A10, 58J50 In this short note we observe, on locally symmetric spaces of higher rank, a connection between the growth indicator function introduced by Quint and the modified critical exponent of the Poincaré series equipped with the polyhedral distance. As a consequence, we provide a different characterization of the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms of the growth indicator function. Moreover, we explore the relationship between these three objects and the temperedness. |
| title | $L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces |
| topic | Spectral Theory 22E40, A7A10, 58J50 |
| url | https://arxiv.org/abs/2311.11770 |