Factorization of rational matrix functions and difference equations (Q2865613)

Based on the authors' abstract: In the beginning of the twentieth century, J.\,Plemelj introduced the notion of factorization of matrix functions. The matrix factorization finds applications in many fields such as diffraction theory, the theory of differential equations and the theory of singular integral operators. However, explicit formulas for the factors of the factorization are known only for a few classes of matrices. In the present paper, we consider a new approach to obtain the factorization of a rational matrix function, relative to the unit circle. The constructed method is based on the relation between the general solution of a homogeneous Riemann-Hilbert problem and a solution of a linear system of difference equations with constant coefficients.