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Behavior of the Singular Integral Along the Real Axis with the Density Vanishing at Infinity Near Infinity

Salimov, R. B.

Published in Lobachevskii Journal of Mathematics

We study the behavior of singular integral along the real axis in the neighborhood of the point at infinity, when its density satisfy Hölder condition in any finite part of the real axis and is continuous function in the neighborhood of the point at infinity, which decreases with the order of decreasing same as the lower then the minus first power ...

The Hilbert problem: The case of infinitely many discontinuity points of coefficients

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...

Publication search with Hilbert boundary value problem as keyword

Behavior of the Singular Integral Along the Real Axis with the Density Vanishing at Infinity Near Infinity

The Hilbert problem: The case of infinitely many discontinuity points of coefficients

Publication search
with Hilbert boundary value problem as keyword