Title: A Szegő theory for rational functions
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav
Issue Date: May-1990
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW131
Abstract: We shall consider nested spaces L_n, n = 0, 1, 2, . . . of rational
functions with n prescribed poles outside the unit disk of the complex
plane. We study orthogonal basis functions of these spaces for
a general positive real measure on the unit circle. In the special
case where all poles are placed at infinity, L_n = Π_n, the polynomials
of degree at most n. Thus the present paper is a study of orthogonal
rational functions, which generalize the orthogonal Szegö
polynomials. We give generalizations of most of the polynomial results: recurrence relations, continued fractions, reproducing kernels
and Christoffel-Darboux relations, approximating properties and relation
with the algorithm of Pick-Nevanlinna, quadrature, etc.
Description: Revised November 1991
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author

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