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

Abstract

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.