#
Publication search

with infinite index as keyword

Shabalin, Pavel Faizov, Rafael
Published in
E3S Web of Conferences

In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index and a boundary condition on a circle for a generalized Cauchy-Riemann equation with a singular coefficient. To solve this problem, we conducted a complete study of the solvability of the Hilbert boundary value problem of the theory of analytic functions with...

Fatykhov, A. Kh. Salimov, R. B. Shabalin, P. L.
Published in
Lobachevskii Journal of Mathematics

We consider Riemann–Hilbert boundary value problem with infinite index in unit disk. Its coefficient is Hölder-continuous everywhere on the unit circle excluding a finite set of points, where its argument has power discontinuities of order less one. The present article is the first research of this version of Hilbert boundary-value problem with inf...

Salimov, R. B. Shabalin, P. L.
Published in
Russian Mathematics

We consider a homogeneous Riemann–Hilbert boundary-value problem for upper halfplane 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...

Salimov, R. B. Shabalin, P. L.
Published in
Russian Mathematics

We consider the Hilbert boundary-value problem for the upper half-plane with a countable set of discontinuity points of coefficient of the boundary condition and with a two-side curling at infinity of a logarithmic order. We obtain formulas for the general solution to the problem.

Salimov, R. B. Shabalin, P. L.
Published in
Siberian Mathematical Journal

We obtain a solution to the Hilbert boundary value problem in the theory of analytic functions on the half-plane in the case that the coefficients of the boundary condition have countably many discontinuity points of the first kind. We elaborate the two substantially different situations: the series consisting of the jumps of the argument of the co...