This article is cited in 3 papers

On solvability of homogeneous Riemann–Hilbert problem with countable set of coefficient discontinuities and two-side curling at infinity of order less than 1/2

R. B. Salimov, P. L. Shabalin

Kazan State University of Architecture and Engineering, Zelenaya str., 1, 420043, Kazan, Russia

Abstract: We consider the homogeneous Riemann–Hilbert problem in the complex upper half-plane with a countable set of coefficients' discontinuities and two-side curling at infinity. In the case the problem index has a power singularity of order less than 1/2, we obtain general solution and completely study the solvability of the problem in a special functional class.

Keywords: Riemann–Hilbert problem, curling at infinity, infinite index, entire functions.

UDC: 517.54

MSC: 30E25, 30E20, 30D10

Received: 09.03.2012

 English version: Ufa Mathematical Journal, 2013, 5:2, 82–93

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