Representation of Operators on Spaces of Holomorphic Functions in $\mathbb{C}^n$
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916961791770624 |
|---|---|
| author | Trybuła, Maria |
| author_facet | Trybuła, Maria |
| contents | We investigate operators between spaces of holomorphic functions in several complex variables. Let $G_1, G_2 \subset \mathbb{C}^n$ be cylindrical domains. We construct a canonical map from the space of bounded linear operators $\mathcal{L}(H(G_1), H(G_2))$ to $H(G_1^b \times G_2)$ and prove that it is a topological isomorphism (Theorem~\ref{pierwsze twierdzenie}). We then establish uniform estimates for operators on bounded, complete $n$-circled domains (Theorem~\ref{thm:4.8}) and show that sequences of operators on smaller domains satisfying suitable uniform bounds uniquely determine a global operator (Theorem~\ref{thm:4.9}). Together, these results provide a unified framework for representing and extending operators on spaces of holomorphic functions in several complex variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation of Operators on Spaces of Holomorphic Functions in $\mathbb{C}^n$ Trybuła, Maria Functional Analysis Complex Variables Primary: 46A32, 32A10, 46E10 Secondary: 32C35, 47A57 We investigate operators between spaces of holomorphic functions in several complex variables. Let $G_1, G_2 \subset \mathbb{C}^n$ be cylindrical domains. We construct a canonical map from the space of bounded linear operators $\mathcal{L}(H(G_1), H(G_2))$ to $H(G_1^b \times G_2)$ and prove that it is a topological isomorphism (Theorem~\ref{pierwsze twierdzenie}). We then establish uniform estimates for operators on bounded, complete $n$-circled domains (Theorem~\ref{thm:4.8}) and show that sequences of operators on smaller domains satisfying suitable uniform bounds uniquely determine a global operator (Theorem~\ref{thm:4.9}). Together, these results provide a unified framework for representing and extending operators on spaces of holomorphic functions in several complex variables. |
| title | Representation of Operators on Spaces of Holomorphic Functions in $\mathbb{C}^n$ |
| topic | Functional Analysis Complex Variables Primary: 46A32, 32A10, 46E10 Secondary: 32C35, 47A57 |
| url | https://arxiv.org/abs/2509.18296 |