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.