Title: Recurrence and asymptotics for orthogonal rational functions on an interval
Authors: Deckers, Karl ×
Bultheel, Adhemar #
Issue Date: Jan-2009
Publisher: Oxford University Press
Series Title: IMA Journal of Numerical Analysis vol:29 issue:1 pages:1-23
Abstract: Let μ be a positive bounded Borel measure on a subset I of the real line, and A = {α_1...,α_n} a sequence of arbitrary complex poles outside I. Suppose {φ_1,...,φ_n} is the sequence of rational functions with poles in A orthonormal on I with respect to μ. First, we are concerned with reducing the number of different coeffcients in the three term recurrence relation satisfied by these orthornormal rational functions. Next, we consider the case in which I = [-1, 1] and μ satisfies the Erdös-Turán condition μ' > 0 a.e. (where μ' is the Radon-Nikodym derivative of the measure μ with respect to the Lebesgue measure), to discuss the convergence of φ_{n+1}(x)/φ_n(x) as n tends to infinity and to derive asymptotic formulas for the recurrence coefficients in the three term recurrence relation. Finally, we give a strong convergence result for φ_n(x) under the more restrictive condition that μ satisfies the Szegö condition (1 - x^2)^{-½} log μ'(x) ∈ L¹[-1; 1].
ISSN: 0272-4979
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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