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

Andreas Debrouwere; Quinten Van Boxstael; Jasson Vindas Diaz

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

Andreas Debrouwere, Quinten Van Boxstael, Jasson Vindas Diaz

Onderzoeksoutput: Voordruk › peer review

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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.

Originele taal-2	Undefined/Unknown
Uitgever	Proceedings of the American Mathematical Society
Aantal pagina's	15
Status	Accepted/In press - 13 mei 2025

Bibliografische nota

15 pages

Keywords

math.AP
math.CV
math.FA
Primary. 35A01, 46E10. Secondary. 35A05, 35A35, 35J05

Toegang tot document

2501.03751v1

Citeer dit

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AB - 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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KW - math.FA

KW - Primary. 35A01, 46E10. Secondary. 35A05, 35A35, 35J05

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

PB - Proceedings of the American Mathematical Society

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