Integral representation of translation-invariant operators on reproducing kernel Hilbert spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908339806404608 |
|---|---|
| author | Bais, Shubham R. Maximenko, Egor A. Naidu, D. Venku |
| author_facet | Bais, Shubham R. Maximenko, Egor A. Naidu, D. Venku |
| contents | We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the translations associated with $G$. We consider the von Neumann algebra of all bounded linear operators acting on $H$ that commute with these translations. Assuming that this algebra is commutative, we represent its elements as integral operators and characterize the corresponding integral kernels. Furthermore, we give W*-algebra structure on the functions associated with the integral kernels. We apply this general scheme to a series of examples, including rotation- or translation-invariant operators in Bergman or Fock spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18850 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integral representation of translation-invariant operators on reproducing kernel Hilbert spaces Bais, Shubham R. Maximenko, Egor A. Naidu, D. Venku Operator Algebras Functional Analysis 47B32, 22D25, 43A25, 47N20, 46L10 We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the translations associated with $G$. We consider the von Neumann algebra of all bounded linear operators acting on $H$ that commute with these translations. Assuming that this algebra is commutative, we represent its elements as integral operators and characterize the corresponding integral kernels. Furthermore, we give W*-algebra structure on the functions associated with the integral kernels. We apply this general scheme to a series of examples, including rotation- or translation-invariant operators in Bergman or Fock spaces. |
| title | Integral representation of translation-invariant operators on reproducing kernel Hilbert spaces |
| topic | Operator Algebras Functional Analysis 47B32, 22D25, 43A25, 47N20, 46L10 |
| url | https://arxiv.org/abs/2504.18850 |