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TW 404

Adhemar Bultheel and Andreas Lasarow
Schur-Nevanlinna sequences of rational functions

Abstract

We study certain sequences of rational functions with poles outside the unit circle. Such kind 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 on the other hand to orthogonal rational functions on the unit circle. We shall see that rational functions belonging to a Schur-Nevanlinna sequence can be used to parameterize the set of all solutions of an interpolation problem of Nevanlinna-Pick type for Schur functions.