On the Riemann–Hilbert problem for analytic functions in circular domains

TitleOn the Riemann–Hilbert problem for analytic functions in circular domains
Publication TypeJournal Article
Year of Publication2016
AuthorsYefimushkin, AS, Ryazanov, VI
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2016.02.013
Issue2
SectionMathematics
Pagination13-16
Date Published2/2016
LanguageRussian
Abstract

The existence of single-valued analytic solutions in a unit disk and multivalent analytic solutions in domains bounded by a finite collection of circles is proved for the Riemann–Hilbert problem with coefficients of sigma finite variation and with boundary data that are measurable with respect to the logarithmic capacity. It is shown that these spaces of solutions have the infinite dimension.

Keywordsanalytic functions, circular domains, Riemann–Hilbert problem
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