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Schur-Nevanlinna sequences of rational functions. (English) Zbl 1152.30037

Authors’ abstract: 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.

MSC:

30E05 Moment problems and interpolation problems in the complex plane
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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