Factorization of Singular Integral Operators with a Carleman Shift via Factorization of Matrix Functions

This paper is devoted to singular integral operators with a linear fractional Carleman shift of arbitrary order preserving the orientation on the unit circle. The main goal is to obtain a special factorization of the operator with the help of a factorization of a related matrix function in a suitable algebra. This factorization allows us to characterize the kernel and the range of the operator under consideration, similarly to the case of singular integral operators without shift.