A linear topological invariant for weighted spaces of holomorphic functions
Functional Analysis
2025-07-01 v1 Complex Variables
Abstract
We study the linear topological invariant 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 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.
Keywords
Cite
@article{arxiv.2506.23695,
title = {A linear topological invariant for weighted spaces of holomorphic functions},
author = {Andreas Debrouwere and Quinten Van Boxstael},
journal= {arXiv preprint arXiv:2506.23695},
year = {2025}
}