On the Riemann–Hilbert problem for analytic functions in circular domains
DOI:
https://doi.org/10.15407/dopovidi2016.02.013Keywords:
analytic functions, circular domains, Riemann–Hilbert problemAbstract
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.
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