Szegő Pairs of Orthogonal Rational Matrix-valued Functions on the Unit Circle

Abstract

We study distinguished pairs of orthonormal systems of rational matrix-valued functions on the unit circle, namely the so-called Szegő pairs. These pairs are determined by an initial condition and a sequence of strictly contractive q × q matrices, which is called the sequence of Szegő parameters. The Szegő parameters contain essential information on the underlying q × q nonnegative Hermitian Borel measure on the unit circle.