сдвиг Карлемана

On One Exceptional Case of the First Basic Three-Element Carleman-Type Boundary Value Problem for Bianalytic Functions in a Circle

Authors: Perelman N. R.

This article considers a non-degenerate (nonreducible to two-element) three-element problem of Carleman type for bianalytic functions in an exceptional case, that is, when one of the coefficients of the boundary condition vanishes at a finite number of contour points. The unit circle is taken as the contour. For this case, an algorithm for solving the problem is constructed, which consists in reducing the boundary conditions of this problem to a system of four Fredholm type equations of the second kind.

A Case of an Explicit Solutions for the Three-element Problem of Carleman Type for Analytic Functions in a Circle

Authors: Perelman N. R.

The article investigates the three-element Carleman boundary value problem in the class of analytic functions, continuous extension to the contour in the Holder sense, when this problem can not be reduced to a two-element boundary value problems . The unit circle is considered as the contour .To be specific, we study a case of inverse shift. In this case, the solution of the problem is reduced to solving a system of two integral equations of Fredholm second kind; thus significantly used the theory of F. D. Gakhov about Riemann boundary value problem for analytic functions.

Three-element problem of Carleman type for bianalitic functions in a circle

Authors: Perelman N. R., Rasulov K. M.

The article is devoted to the investigation of three-element boundary value problem of Carleman type for bianalytic functions. A constructive method for solution in a circle was found for the case when the problem was not reducible to a two-element boundary value problems without a shift.