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

2015/10/06 by Artem S. Efimushkin, Vladimir Ryazanov, Efimushkin, A. S. +1
Mathematics · #Analytic and geometric function theory #Meromorphic and Entire Functions #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1510.01513

Abstract

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

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