Multipliers on Spaces of Holomorphic Functions on Runge Domains in $\mathbb{C}^n
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911169390837760 |
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| author | Trybuła, Maria |
| author_facet | Trybuła, Maria |
| contents | We investigate multipliers on the space of holomorphic functions $H(Ω)$, where $Ω\subset \mathbb{C}^n$ is an open set. For Runge domains, we characterize these multipliers as convolutions with analytic functionals. Additionally, we explore Cartesian product domains, providing a representation of multipliers through germs of holomorphic functions. Finally, we identify the appropriate topology for analytic functionals, establishing a topological isomorphism with multipliers by utilizing the topology of uniform convergence on bounded sets inherited from the space of endomorphisms on $H(Ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multipliers on Spaces of Holomorphic Functions on Runge Domains in $\mathbb{C}^n Trybuła, Maria Functional Analysis Complex Variables 47B91, 46F15, 44A35, 32D15, 32A10 We investigate multipliers on the space of holomorphic functions $H(Ω)$, where $Ω\subset \mathbb{C}^n$ is an open set. For Runge domains, we characterize these multipliers as convolutions with analytic functionals. Additionally, we explore Cartesian product domains, providing a representation of multipliers through germs of holomorphic functions. Finally, we identify the appropriate topology for analytic functionals, establishing a topological isomorphism with multipliers by utilizing the topology of uniform convergence on bounded sets inherited from the space of endomorphisms on $H(Ω)$. |
| title | Multipliers on Spaces of Holomorphic Functions on Runge Domains in $\mathbb{C}^n |
| topic | Functional Analysis Complex Variables 47B91, 46F15, 44A35, 32D15, 32A10 |
| url | https://arxiv.org/abs/2509.18287 |