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https://doi.org/10.15480/882.2798
Publisher DOI: | 10.1007/s13398-020-00863-x | arXiv ID: | 1901.01235 | 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) | 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 | Journal: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales | Institute: | Mathematik E-10 | Document Type: | Article | Project: | Projekt DEAL | License: | ![]() |
Appears in Collections: | Publications with fulltext |
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Kruse2020_Article_ParameterDependenceOfSolutions.pdf | Verlag-PDF | 410,04 kB | Adobe PDF | View/Open![]() |
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