Title: Favard theorem for reproducing kernels
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: Feb-1995
Publisher: Elsevier
Series Title: Journal of computational and applied mathematics vol:57 issue:1-2 pages:57-76
Abstract: Consider for n=0,1,... the nested spaces L_n of rational functions of degree n at most with given poles 1/ã_i, |a_i|<1, i=1,...,n. Let L=U_{0..∞} L_n. Given a finite positive measure µ on the unit circle, we associate with it an inner product on L by <f,g> = ∫ f g~dµ. Suppose k_n(z,w) is the reproducing kernel for L_n, i.e., < f(z),k_n(z,w)> = f(w), for all f in L_n, |w|<1, then it is known that they satisfy a coupled recurrence relation. In this paper we shall prove a Favard type theorem which says that if you have a sequence of kernel functions k_n(z,w) which are generated by such a recurrence, then there will be a measure µ supported on the unit circle so that kn is the reproducing kernel for L_n. The measure is unique under certain extra conditionson the points a_i.
ISSN: 0377-0427
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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