Regularization method for a class of dual series equations in diffraction theory

The paper is devoted to the development of a regularization technique for a class of dual series equations which appear in 2D problems of the wave diffraction on metal screens located at the interface between anisotropic dielectric media, some contact problems in the theory of elasticity, etc. An idea of equivalent reformulation of these equations in terms of the conjugation problem of analytic functions, which is the Riemann-Hilbert problem for an unclosed contour forms the basis of the suggested method of regularization