Title: A Favard theorem for orthogonal rational functions on the unit circle
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: 1992
Publisher: Baltzer, Bussum
Series Title: Numerical Algorithms vol:3 pages:81-89
Conference: Internat. Congr. Extrapolation and Rational Approx location:La Laguna, Tenerife, SP date:January 1992
Abstract: We consider for n=0,1,... the nested spaces L_n of rational functions of degree n at most with given poles 1/ã_i, |ã_i|<1, i=1,...,n. It is known that, given a measure supported on the unit circle, it is possible to generate a nested orthogonal basis fn in Ln of rationals. These satisfy a recurrence relation that generalizes the recurrence for Szegö polynomials.

In this paper we shall prove a Favard type theorem which says that if you have a sequence of rational functions fn in L_n which are generated by such a recurrence,then there will be a measure µ supported on the unit circle to which they are orthogonal. We shall give a sufficient condition for the uniqueness of this measure.
ISSN: 1017-1398
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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