On a class of singular integral equation with the linear fractional Carleman shift and the degenerate kernel

Abstract

This article deals with the solvability, the explicit solutions of a class of singular integral equations with a linear-fractional Carleman shift and the degenerate kernel on the unit circle by means of the Riemann boundary value problem and of a system of linear algebraic equations. All cases about index of the coefficients in the equations are considered in detail.