A theorem of Strichartz for multipliers on homogeneous trees
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916128412925952 |
|---|---|
| author | Rano, Sumit Kumar Sarkar, Rudra P. |
| author_facet | Rano, Sumit Kumar Sarkar, Rudra P. |
| contents | A theorem of Strichartz states that if a uniformly bounded bi-infinite sequence of functions on the Euclidean spaces, satisfies the condition that the Laplacian acting on a function in this sequence yields the next one, then each function in this sequence is an eigenfunction of the Laplacian. We consider a generalization of this result for homogeneous trees, where we replace bounded functions by tempered distributions and the Laplacian by multiplier operators acting on the tempered distributions. After establishing the result in this general context, we narrow our focus to specific cases, which includes important examples of multiplier operators such as heat and Schrödinger operator, ball and sphere averages of function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A theorem of Strichartz for multipliers on homogeneous trees Rano, Sumit Kumar Sarkar, Rudra P. Classical Analysis and ODEs Functional Analysis Primary 43A85 Secondary 20E08, 39A12, 43A90 A theorem of Strichartz states that if a uniformly bounded bi-infinite sequence of functions on the Euclidean spaces, satisfies the condition that the Laplacian acting on a function in this sequence yields the next one, then each function in this sequence is an eigenfunction of the Laplacian. We consider a generalization of this result for homogeneous trees, where we replace bounded functions by tempered distributions and the Laplacian by multiplier operators acting on the tempered distributions. After establishing the result in this general context, we narrow our focus to specific cases, which includes important examples of multiplier operators such as heat and Schrödinger operator, ball and sphere averages of function. |
| title | A theorem of Strichartz for multipliers on homogeneous trees |
| topic | Classical Analysis and ODEs Functional Analysis Primary 43A85 Secondary 20E08, 39A12, 43A90 |
| url | https://arxiv.org/abs/2402.10703 |