A linear topological invariant for weighted spaces of holomorphic functions

2025/06/30 by Debrouwere, Andreas, Van Boxstael, Quinten
#35A01 #46A63 #46E10 #46E40 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2506.23695

Abstract

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.

Citations

• On the surjectivity of the Cauchy-Riemann and Laplace operators on weighted spaces of smooth functions
• Sequence space representations for spaces of entire functions with rapid decay on strips

Related

• On the surjectivity of the Cauchy-Riemann and Laplace operators on weighted spaces of smooth functions
• Weighted spaces of vector-valued functions and the ε-product
• Dual Approach to Certain Questions for Weighted Spaces of Holomorphic Functions
• Nearly Holomorphic Functions and Relative Discrete Series of Weighted L²-Spaces on Bounded Symmetric Domains
• Topologies on the space of holomorphic functions