Applications of operator equalities to singular integral operators and to Riemann boundary value problems

Abstract

In the first part of this article (Section 2), we consider a Riemann boundary value problem with shift and piecewise constant coefficients. In the second part (Section 3), we consider a matrix characteristic singular integral operators with piecewise constant coefficients of a special structure. Simplicity of the shift and the coefficients under consideration permits us to obtain conditions under which the Riemann boundary value problem admits an unique solution and to study the invertibility of the matrix characteristic singular integral operators.