Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions

Karsten Kruse

doi:10.1007/s13398-020-00863-x

Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions

Karsten Kruse^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

3 Citations (Scopus)

2 Downloads (Pure)

Abstract

Let Ω be an open subset of R² and E a complete complex locally convex Hausdorff space. The purpose of this paper is to find conditions on certain weighted Fréchet spaces EV(Ω) of smooth functions and on the space E to ensure that the vector-valued Cauchy–Riemann operator ∂¯ : EV(Ω, E) → EV(Ω, E) is surjective. This is done via splitting theory and positive results can be interpreted as parameter dependence of solutions of the Cauchy–Riemann operator.

Original language	English
Article number	141
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	114
Issue number	3
DOIs	https://doi.org/10.1007/s13398-020-00863-x
Publication status	Published - 1 Jul 2020
Externally published	Yes

Keywords

Cauchy–Riemann
Parameter dependence
Smooth
Solvability
Vector-valued
Weight

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10.1007/s13398-020-00863-xLicence: CC BY

s13398-020-00863-xFinal published version, 486 KBLicence: CC BY

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KW - Cauchy–Riemann

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KW - Vector-valued

KW - Weight

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ER -

Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions

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Keywords

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