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SCHUR–NEVANLINNA SEQUENCES OF RATIONAL FUNCTIONS

Published online by Cambridge University Press:  08 January 2008

Adhemar Bultheel  and
Andreas Lasarow
Adhemar Bultheel
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001 Heverlee (Leuven), Belgium (adhemar.bultheel@cs.kuleuven.be; andreas.lasarow@cs.kuleuven.be)
Andreas Lasarow
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001 Heverlee (Leuven), Belgium (adhemar.bultheel@cs.kuleuven.be; andreas.lasarow@cs.kuleuven.be)
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Abstract

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We study certain sequences of rational functions with poles outside the unit circle. Such kinds of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur–Nevanlinna algorithm for Schur functions on the one hand, and to orthogonal rational functions on the unit circle on the other. We shall see that rational functions belonging to a Schur–Nevanlinna sequence can be used to parametrize the set of all solutions of an interpolation problem of Nevanlinna–Pick type for Schur functions.

Keywords

Primary 30E05Secondary 42C05Nevanlinna–Pick interpolation problemSchur functionsrational functionsChristoffel–Darboux formulaeSchur–Nevanlinna algorithmSchur parameters
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 571 - 596
Copyright
Copyright © Edinburgh Mathematical Society 2007