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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.
DOI: 10.15480/882.2798
ISSN: 1579-1505
Institute: Mathematik E-10 
Type: (wissenschaftlicher) Artikel
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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