Factorization of J-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions

Abstract

We prove that a 2×2 matrix polynomial which is J-unitary on the real line can be written as a product of normalized elementary J-unitary factors and a J-unitary constant. In the second part we give an algorithm for this factorization using an analog of the Schur transformation.