A linear topological invariant for weighted spaces of holomorphic functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916817162731520 |
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| author | Debrouwere, Andreas Van Boxstael, Quinten |
| author_facet | Debrouwere, Andreas Van Boxstael, Quinten |
| contents | We study the linear topological invariant $(Ω)$ for a class of Fréchet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight function systems. We obtain a complete characterization of the property $(Ω)$ for such spaces in terms of an explicit condition on the defining weight function systems. As an application, we investigate the surjectivity of the Cauchy-Riemann operator on certain weighted spaces of vector-valued smooth functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A linear topological invariant for weighted spaces of holomorphic functions Debrouwere, Andreas Van Boxstael, Quinten Functional Analysis Complex Variables 46E10, 46A63, 46E40, 35A01 We study the linear topological invariant $(Ω)$ for a class of Fréchet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight function systems. We obtain a complete characterization of the property $(Ω)$ for such spaces in terms of an explicit condition on the defining weight function systems. As an application, we investigate the surjectivity of the Cauchy-Riemann operator on certain weighted spaces of vector-valued smooth functions. |
| title | A linear topological invariant for weighted spaces of holomorphic functions |
| topic | Functional Analysis Complex Variables 46E10, 46A63, 46E40, 35A01 |
| url | https://arxiv.org/abs/2506.23695 |