Title: A density problem for orthogonal rational functions
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: May-1999
Publisher: Elsevier
Series Title: Journal of computational and applied mathematics vol:105 issue:1-2 pages:199-212
Abstract: Let {a_n:n=1...∞} be a sequence of points in the open unit disk in the complex plane and let

B_0 = 1 and B_n(z) = ∏_{k=0...n} ã_k/|a_k| [(a_k-z)/( 1-ã_kz)], n=1,2,...,
(ã_k/|a_k| = -1 when a_k = 0). We put

L = span{B_n : n=0,1,2,...}
and we consider the following "moment" problem:

Given a positive-definite Hermitian inner product <.,.> on L x L, find a non-decreasing function µ on [-π,π] (or a positive Borel measure µ on [-π,π)) such that

<f,g> = ∫_{x=-π..π}f(e^{it})g(e^{it})~ dµ(t) for f,g in L.
We give a necessary and sufficient condition (called "N-extremality") on a solution µ of the moment problem in order that L is dense in L_µ^2
ISSN: 0377-0427
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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