Details

Autor(en) / Beteiligte

• Fritzsche, Bernd
• Kirstein, Bernd
• Lasarow, Andreas

Titel

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

Ist Teil von

• Mathematische Nachrichten, 2006-04, Vol.279 (5-6), p.513-542

Ort / Verlag

Berlin: WILEY-VCH Verlag

Erscheinungsjahr

2006

Quelle

Wiley Online Library

Beschreibungen/Notizen

• 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 jqq ‐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)