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arXiv · 2506.23695

A linear topological invariant for weighted spaces of holomorphic functions

Andreas Debrouwere·Quinten Van Boxstael
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Abstract

We study the linear topological invariant $(\Omega)$ for a class of Fr\'echet 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 $(\Omega)$ 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.

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Andreas Debrouwere, Quinten Van Boxstael. 2025-06-30. A linear topological invariant for weighted spaces of holomorphic functions. https://arxiv.org/abs/2506.23695

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