Orthogonal rational matrix-valued functions on the unit circle: Recurrence relations and a Favard-type theorem

摘要

This paper contains further steps towards a Szego theory for orthogonal rational matrix-valued functions on the unit circle T. It continues the investigations started in [18]-[20]. Hereby we are guided by former work of Bultheel, Gonzalez-Vera, Hendriksen, and Njastad on scalar orthogonal rational functions on the one side and by research of Delsarte, Genin, and Kamp on matrix polynomials on the other side. In this paper we derive recursion formulas for Christoffel-Darboux pairs of rational matrix functions which lead us to j{sub}(qq)-recursively connected pairs of rational matrix functions. Moreover, we prove a Favard-type theorem for rational matrix functions.