arXiv subjects

Quinten Van Boxstael

Publications and source records attributed to Quinten Van Boxstael.

2 recordsLinked to original sources

arXiv2025

On the surjectivity of the Cauchy-Riemann and Laplace operators on weighted spaces of smooth functions

We study the surjectivity of the Cauchy-Riemann and Laplace operators on certain weighted spaces of smooth functions of rapid decay on strip-like domains in the complex plane that are defined via weight function systems. We fully characterize when these operators are surjective on such function spaces in terms of a growth condition on the defining weight function systems.

math.AP↗

arXiv2025

A linear topological invariant for weighted spaces of holomorphic functions

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.

math.FA↗