Approximate factorization for a class of second-order matrix functions

Abstract

The notion of approximate factorization of a Hölder matrix function on a simple smooth closed contour is introduced. The elements of a (2 × 2)-matrix function of a special form are approximated by polynomials in z and 1/z. Sufficient conditions for the vanishing of the partial indices of the approximating matrix function are found. Factorization of the approximating matrix function is explicitly constructed.