A constructive method of solution of a system of singular integral equations with constant coefficients in an interval (Q2753512)

A constructive method of solution of a system of singular integral equations (SSIE) with constant coefficients in the interval \([-1, 1]\) is suggested. The method consists in substitution of the variables \(x=\tanh\alpha/2,y=\tanh\beta/2\) in the original equations and a subsequent application of the Fourier transform to the obtained equations in the interval \((-\infty, \infty)\). The method enables one: (i) to solve the SSIE with constant coefficients in wider spaces than described in the literature; (ii) to apply to the solution of the SSIE with constant coefficients a uniform approach, related to the theory of linear differential equations; (iii) to reduce the number of algebraical operations in the determination of the general structure of the solution of an SSIE with constant coefficients, and this reduction is essential for systems of large dimension. The problem of oscillating and non-oscillating solutions of SSIE is investigated.