Rotational symmetries of domains and orthogonality relations
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_ | 1866929681379360768 |
|---|---|
| author | Ganguly, Soumya Treuer, John N. |
| author_facet | Ganguly, Soumya Treuer, John N. |
| contents | Let $Ω\subset \mathbb{C}^n$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $Ω$ to be Reinhardt, complete Reinhardt, circular or Hartogs in terms of the orthogonality relations of the monomials with respect to their $L^2$-inner products and their $L^2$-norms. More generally, we give sufficient conditions for $Ω$ to be invariant under a linear group action of an $r$-dimensional torus, where $r \in \{1,\ldots, n\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01115 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rotational symmetries of domains and orthogonality relations Ganguly, Soumya Treuer, John N. Complex Variables 32Q06, 44A60, 32A36 Let $Ω\subset \mathbb{C}^n$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $Ω$ to be Reinhardt, complete Reinhardt, circular or Hartogs in terms of the orthogonality relations of the monomials with respect to their $L^2$-inner products and their $L^2$-norms. More generally, we give sufficient conditions for $Ω$ to be invariant under a linear group action of an $r$-dimensional torus, where $r \in \{1,\ldots, n\}$. |
| title | Rotational symmetries of domains and orthogonality relations |
| topic | Complex Variables 32Q06, 44A60, 32A36 |
| url | https://arxiv.org/abs/2410.01115 |