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

Publikationstyp
Journal Article
Publikationsdatum
2020-05-30
Sprache
English
Author
Kruse, Karsten 
Institut
Mathematik E-10 
DOI
10.15480/882.2798
TORE-URI
http://hdl.handle.net/11420/6292
Lizenz
https://creativecommons.org/licenses/by/4.0/
Enthalten in
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 
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
10.1007/s13398-020-00863-x
Scopus ID
2-s2.0-85085772829
ArXiv ID
1901.01235
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.
Schlagworte
Cauchy–Riemann
Parameter dependence
Smooth
Solvability
Vector-valued
Weight
DDC Class
510: Mathematik
Projekt(e)
Projekt DEAL