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

✍ Scribed by Bernd Fritzsche; Bernd Kirstein; Andreas Lasarow

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 384 KB
• Volume: 279
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310376

✦ Synopsis

Abstract

This paper contains further steps towards a Szegö 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, González–Vera, Hendriksen, and Njåstad 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~qq~ ‐recursively connected pairs of rational matrix functions. Moreover, we prove a Favard‐type theorem for rational matrix functions. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)