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Orthogonal rational matrix-valued functions on the unit circle

✍ Scribed by Bernd Fritzsche; Bernd Kirstein; Andreas Lasarow

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
391 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

This paper contains first steps towards a Szegö theory of orthogonal rational matrix‐valued functions on the unit circle 𝕋. 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 investigations of Delsarte, Genin, and Kamp on orthogonal matrix polynomials on the other side. An essential characteristic of our matricial orthogonalization procedure is marked by an intensive interplay between left and right matrix‐valued inner products generated by a nonnegative Hermitian Borel measure on the unit circle. The main feature of our approach is the distinguished role of Christoffel‐Darboux formulas. We consider pairs of rational matrix‐valued functions linked via Christoffel‐Darboux type relations as an own subject. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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