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Golusin-Krylov Formulas in Complex Analysis

  • This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.

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Metadaten
Author details:Alexander ShlapunovORCiDGND, Nikolai Nikolaevich TarkhanovORCiDGND
URN:urn:nbn:de:kobv:517-opus4-102774
Title of parent work (German):Preprints des Instituts für Mathematik der Universität Potsdam
Publication series (Volume number):Preprints des Instituts für Mathematik der Universität Potsdam (6 (2017) 2)
Publisher:Universitätsverlag Potsdam
Place of publishing:Potsdam
Publication type:Preprint
Language:English
Year of first publication:2017
Publication year:2017
Publishing institution:Universität Potsdam
Publishing institution:Universitätsverlag Potsdam
Release date:2017/02/08
Tag:Cauchy problem; analytic continuation; integral formulas
Volume:6
Issue:2
Number of pages:25
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:32-XX SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES (For infinite-dimensional holomorphy, see 46G20, 58B12) / 32Dxx Analytic continuation / 32D15 Continuation of analytic objects
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J56 Boundary value problems for first-order elliptic systems
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K15 Initial value problems for second-order parabolic equations
Collection(s):Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2017
License (German):License LogoKeine öffentliche Lizenz: Unter Urheberrechtsschutz
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