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Title: Orthogonal rational functions and interpolatory product rules on the unit circle. II. Quadrature and convergence
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: 1998
Publisher: Oldenbourg, Munich
Series Title: Analysis vol:18 pages:185-200
Abstract: Let R be the space of rational functions with poles among {a_k,1/ã_k:k=0,...,∞} with a_0 = 0 and |a_k|<1, k ≤ 1. We consider a sequence {R_n:n=0,...,∞} of nested subspaces with U_{n=0,...,∞} R_n = R. First we recall from part I how to find orthogonal bases for R for a positive measure on the unit circle. These are used in the construction of interpolatory quadrature rules for integrals with respect to a complex measure on the unit circle. Integration for the (2n+1)-point rule is exact for all f in R_n. Also their convergence is discussed as n → ∞. Finally we discuss the convergence of multipoint rational approximants to the Riesz-Herglotz transform associated with such a complex measure.
URI: 
ISSN: 0174-4747
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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