Title: Boundary asymptotics for orthogonal rational functions on the unit circle
Authors: Bultheel, Adhemar ×
Van gucht, Patrick #
Issue Date: May-2000
Publisher: D. Reidel
Series Title: Acta applicandae mathematicae vol:61 issue:1-3 pages:333-349
Conference: International Conference on Rational Approximation and Applications location:Antwerp, Belgium date:6-11 June 1999
Abstract: Let w(t) be a positive weight function on the unit circle of the complex plane. For a sequence of points {a_k:k=1...∞} included in a compact subset of the unit disk, we consider the orthogonal rational functions φn that are obtained by orthogonalization of the sequence {1,z/π_1,z^2/π_2,...} where π_k(z) = ∏_{j=1...k} (1-ã_jz), with respect to the inner product
< f,g > = (1/2π)∫_{t=-π...π} f(e^{it})g(e^{it})*w(t)dt.
We discuss in this paper the behaviour of φ_n(t) for |t|=1 and n → ∞ under certain conditions. The main condition on the weight is that it satisfies a Lipschitz-Dini condition and that it is bounded away from zero. This generalizes a theorem given by Szegö in the polynomial case, that is when all a_k=0.
ISSN: 0167-8019
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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