A linear topological invariant for weighted spaces of holomorphic functions
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.
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