Published in Russian Mathematics
We study behavior of singular integral at neighborhood of the point at infinity. Its density satisfies the Hölder condition on the any finite part of the real axis, and at the infinity point it vanishes as power of logarithm with exponent lesser than −1.
Published in Russian Mathematics
We propose a formula for the conformalmapping of the upper half-plane onto a polygonal domain, which generalizes the Schwarz–Christoffel equation. It is obtained by terms of partial solution to the Hilbert boundary-value problem with a countable set of singularity points of the coefficients including a turbulence of logarithmic type at the infinity...
Published in Russian Mathematics
We propose a modification of the approach proposed by us in Russian Mathematics (Iz. VUZ) 44 (2), 58–62 (2000) for the solution of the Hilbert boundary-value problem for an analytic function in a multiconnected circular domain. This approach implies the solution of the corresponding homogeneous problem including the determination of an analytic fun...
Published in Russian Mathematics
We consider the Hilbert boundary-value problem with a finite index for the case, when the coefficients in the boundary condition have two infinite sequences of discontinuity points of the first kind. We obtain a formula for the general solution and study the solvability issues.
Published in Mathematical Notes
In this paper, we obtain a generalization of the method of regularizing multipliers for the solution of the Hilbert boundary-value problem with finite index in the theory of analytic functions to the case of an infinite power-behaved index. This method is used to obtain a general solution of the homogeneous Hilbert problem for the half-plane, a sol...
