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Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions
Citation Link: https://doi.org/10.15480/882.2798
Publikationstyp
Journal Article
Date Issued
2020-05-30
Sprache
English
Author(s)
Institut
TORE-DOI
TORE-URI
Volume
114
Issue
3
Article Number
141
Citation
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 3 (114): 141 (2020-07-01)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Springer
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.
Subjects
Cauchy–Riemann
Parameter dependence
Smooth
Solvability
Vector-valued
Weight
DDC Class
510: Mathematik
Publication version
publishedVersion
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Kruse2020_Article_ParameterDependenceOfSolutions.pdf
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