Dual pairs of orthogonal systems of rational matrix-valued functions on the unit circle

Abstract

SummaryWe analyse certain dual pairs of orthogonal systems of rational matrix-valued functions with poles not located on the unit circle. The rational matrix-valued functions belonging to such kind of pairs are recursively connected similar as the functions of the first and the second kind in the classical theory of orthogonal polynomials on the unit circle. We present some basic facts on these dual pairs and, in particular, we show that the rational matrix-valued functions in question admit specific integral representations.