Pointwise and uniform bounds for functions of the Laplacian on non-compact symmetric spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910589183328256 |
|---|---|
| author | Kuznetsova, Yulia Song, Zhipeng |
| author_facet | Kuznetsova, Yulia Song, Zhipeng |
| contents | Let $L$ be the distinguished Laplacian on the Iwasawa $AN$ group associated with a semisimple Lie group $G$. Assume $F$ is a Borel function on $\mathbb{R}^+$. We give a condition on $F$ such that the kernels of the functions $F(L)$ are uniformly bounded. This condition involves the decay of $F$ only and not its derivatives. By a known correspondence, this implies pointwise estimates for a wide range of functions of the Laplace-Beltrami operator on symmetric spaces. In particular, when $G$ is of real rank one and $F(x)={\rm e}^{it\sqrt x}ψ(\sqrt x)$, our bounds are sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02688 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pointwise and uniform bounds for functions of the Laplacian on non-compact symmetric spaces Kuznetsova, Yulia Song, Zhipeng Analysis of PDEs Functional Analysis 22E30, 42B15, 35L05, 43A85, 43A90 Let $L$ be the distinguished Laplacian on the Iwasawa $AN$ group associated with a semisimple Lie group $G$. Assume $F$ is a Borel function on $\mathbb{R}^+$. We give a condition on $F$ such that the kernels of the functions $F(L)$ are uniformly bounded. This condition involves the decay of $F$ only and not its derivatives. By a known correspondence, this implies pointwise estimates for a wide range of functions of the Laplace-Beltrami operator on symmetric spaces. In particular, when $G$ is of real rank one and $F(x)={\rm e}^{it\sqrt x}ψ(\sqrt x)$, our bounds are sharp. |
| title | Pointwise and uniform bounds for functions of the Laplacian on non-compact symmetric spaces |
| topic | Analysis of PDEs Functional Analysis 22E30, 42B15, 35L05, 43A85, 43A90 |
| url | https://arxiv.org/abs/2409.02688 |