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

Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.2798

Publisher DOI:	10.1007/s13398-020-00863-x
Title:	Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions
Language:	English
Authors:	Kruse, Karsten
Keywords:	Cauchy–Riemann;Parameter dependence;Smooth;Solvability;Vector-valued;Weight
Issue Date:	30-May-2020
Publisher:	Springer
Source:	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 3 (114): 141 (2020-07-01)
Journal or Series Name:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales
Abstract (english):	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.
URI:	http://hdl.handle.net/11420/6292
DOI:	10.15480/882.2798
ISSN:	1579-1505
Institute:	Mathematik E-10
Type:	(wissenschaftlicher) Artikel
License:	CC BY 4.0 (Attribution)
Appears in Collections:	Publications with fulltext