Operator equalities for singular integral operators and their applications

Abstract

The article consists of tow parts. In the first, we stablish a relation between the singular integral operators on the unit circle with a model orientation reversing shith operator and the singular integral operators on the unit circle with a model orientation preserving shift operator. In the secund part, a Rieman boundary value problem with shift is considered. We reduce this problem to a matrix characteristic single integral operator without shift.