Title: Orthogonal rational functions with poles on the unit-circle
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: Feb-1994
Publisher: Academic Press
Series Title: Journal of mathematical analysis and applications vol:182 issue:1 pages:221-243
Abstract: Let {α_n} be a sequence of (not necessarily distinct) points on the unit circle T= {z in C: |z| = 1). Set L_n = Span {1, 1/ω_1, ..., 1/ω_n}, L = U_{n=0..∞} L_n, where we have used the notation ω_n = ∏_{k=1..n} (z - α_k). Let M be a positive linear functional defined on the space L · L with M(R) real for functions that are real on T. Define <R, S> = M(R(z) S(1/z)) for R, S* in L. (In particular if M is given as M(R) ∫_{-π..π} R(e^{iθ}) dµ(θ) for some measure µ, then <R, S> = ∫_{-π..π} R(e^{iθ}) S(e^{iθ})dµ(θ)*.) Let the orthogonal system {φ_n} be obtained from {1/ω_n} by orthogonalization. Three-term recurrence relations, quadrature formulas, moment theory, and interpolation properties connected with the functional M and the system {φ_n} are discussed.
ISSN: 0022-247X
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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