Approximate Factorization for One Class of Second-Order Matrix Functions

Approximate factorization of Holder matrix function on a simple smooth closed contour has been defined. Components for one class of the 2×2 matrix function have been approximated by polynomials in z and 1/ z. Sufficient conditions have been found for zero equality of the partial indices of the approximating matrix function. Factorization of the approximating matrix function has been constructed in an explicit form.