This article is cited in 2 papers

On solvability of homogeneous Riemann–Hilbert problem with discontinuities of coefficients and two-side curling at infinity of a logarithmic order

R. B. Salimov, P. L. Shabalin

Chair of Higher Mathematics, Kazan State Architecture and Building University, 1 Zelyonaya str., Kazan, 420043 Russia

Abstract: We consider the homogeneous Riemann–Hilbert boundary-value problem for upper half-plane in the situation where its coefficients have countable set of discontinuities of jump type and two-side curling at infinity of a logarithmic order. We obtain general solution and describe completely its solvability in a special class of functions for the case where the index of the problem has power singularity of a logarithmic order.

Keywords: Riemann–Hilbert boundary-value problem, curling at infinity, infinite index, entire functions of zero order.

UDC: 517.544

Received: 26.06.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:1, 30–41

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