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arXiv · 2501.03751

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

Andreas Debrouwere·Quinten Van Boxstael·Jasson Vindas
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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.

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Andreas Debrouwere, Quinten Van Boxstael, Jasson Vindas. 2025-01-07. On the surjectivity of the Cauchy-Riemann and Laplace operators on weighted spaces of smooth functions. https://doi.org/10.1090/proc/17375

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