Factorization of analytic matrix-valued functions (Q1567782)

The article is devoted to the problem of calculating the partial indices and the Wiener-Hopf factorization of analytic matrix-valued functions. The method of finding the divisors of an analytic matrix-valued function \(a(t)\) that generate the zeros of \(\text{det }a(t)\) is introduced. The method is based upon properties of indices and essential polynomials of families of matrices, an approach for factorization of analytic matrix-valued functions.