SCHUR–NEVANLINNA SEQUENCES OF RATIONAL FUNCTIONS

Adhemar Bultheel, Andreas Lasarow

Type: Article

Publication Date: 2007-10-01

Citations: 5

DOI: https://doi.org/10.1017/s0013091504001063

Abstract

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.

Locations

Proceedings of the Edinburgh Mathematical Society - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF
Lirias (KU Leuven) - View - PDF

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Works Cited by This (16)

Action	Title	Year	Authors
+	Interpolation of Rational Matrix Functions	1990	Joseph A. Ball Israel Gohberg Leiba Rodman
+	Matricial version of the classical Schur problem	1992	Vladimir K. Dubovoj Bernd Kirstein Bernd Fritzsche
+	The Classical Moment Problem and Some Related Questions in Analysis	2020	Н. И. Ахиезер
+ PDF Chat	Orthogonal Rational Functions	1999	Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad
+	On the multiple Nevanlinna-Pick matrix interpolation in the class Cp and the Carathéodory matrix coefficient problem	1998	Gong-Ning Chen Yong-Jian Hu
+ PDF Chat	Nevanlinna parametrizations for the extended interpolation problem	1990	Sechiko Takahashi
+	ANALYTIC THEORY OF A CLASS OF INTERPOLATION PROBLEMS	1984	I. V. Kovalishina
+	Multiple point interpolation in Nevanlinna classes	1997	Harald Woracek
+	The Commutant Lifting Approach to Interpolation Problems	1990	Ciprian Foiaş A. E. Frazho
+	The Nevanlinna–Pick Problem for Matrix-Valued Functions	1979	P. Delsarte Y. Genin Y. Kamp