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Szegő Pairs of Orthogonal Rational Matrix-valued Functions on the Unit Circle

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Operator Theory and Indefinite Inner Product Spaces

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 163))

Abstract

We study distinguished pairs of orthonormal systems of rational matrix-valued functions on the unit circle, namely the so-called Szegő pairs. These pairs are determined by an initial condition and a sequence of strictly contractive q × q matrices, which is called the sequence of Szegő parameters. The Szegő parameters contain essential information on the underlying q × q nonnegative Hermitian Borel measure on the unit circle.

The work of the third author of the present paper was supported by the German Academy of Natural Scientists Leopoldina by means of the Federal Ministry of Education and Research on badge BMBF-LPD 9901/8-88.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10, D-04109, Leipzig, Germany

    Bernd Fritzsche & Bernd Kirstein

  2. Departement Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001, Heverlee (Leuven), Belgium

    Andreas Lasarow

Authors
  1. Bernd Fritzsche
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  2. Bernd Kirstein
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  3. Andreas Lasarow
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow, G1 1XH, UK

    Matthias Langer

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8-10 / 101, 1040, Wien, Austria

    Annemarie Luger  & Harald Woracek  & 

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Dedicated to Professor Heinz Langer

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Fritzsche, B., Kirstein, B., Lasarow, A. (2005). Szegő Pairs of Orthogonal Rational Matrix-valued Functions on the Unit Circle. In: Langer, M., Luger, A., Woracek, H. (eds) Operator Theory and Indefinite Inner Product Spaces. Operator Theory: Advances and Applications, vol 163. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7516-7_8

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