Dual Szegő pairs of sequences of rational matrix-valued functions
This paper is the dual of [\textit{B. Fritzsche, B. Kirstein} and \textit{A. Lasarow}, ``Szegő pairs of orthogonal rational matrix-valued functions on the unit circle''. in Operator theory and indefinite inner product spaces. Basel: Birkhäuser. Operator Theory: Adv. Appl. 163, 163--189 (2006; Zbl 1120.42014)]. Matrix-valued rational functions with prescribed poles, orthogonal with respect to a matrix-valued measure supported on the complex unit circle satisfy a Szegő type of recurrence relation, characterized by matrix-valued Szegő parameters. In these relations, left and right matrix-valued orthogonal rational functions (MORF) are mixed, hence they form Szegő pairs. Changing the sign of the Szegő parameters gives a dual Szegő pair. These dual pairs also satisfy some Christoffel-Darboux relations and they turn out to be MORF for a (matrix-valued) measure that is closely related to the orthogonality measure of the MORF. Also the relation between the recurrence relation and Potapov's J-theory is given.
scientific article; zbMATH DE number 5164012
scientific article