Title: Rational wavelets on the real line
Authors: Bultheel, Adhemar ×
González-Vera, Pablo #
Issue Date: 2000
Publisher: M. Dekker
Series Title: Numerical functional analysis and optimization vol:21 issue:1-2 pages:77-96
Conference: Fourier Analysis and its Applications (FAA98) location:Kuwait City, Kuwait date:3-6 May 1998
Abstract: Suppose {φ_k:k=0,...,n} is an orthonormal basis for the function space L_n of polynomials or rational functions of degree n with prescribed poles. Suppose n=2^s and set V_s=L_n. Then k_n(z,w)=∑_{k=0,...,n} φ_k(z)[φ_k(w)}]~, is a reproducing kernel for V_s. For fixed w, such reproducing kernels are known to be functions localized in the neighborhood of z=w. Moreover, by an appropriate choice of the parameters {ξ_{nk}:k=0,...,n}, the functions {φ_{n,k}(z)=k_n(z,ξ_{nk}):k=0,...n} will be an orthogonal basis for V_s. The orthogonal complement W_s=V_{s+1} - V_s is spanned by the functions {ψ_{n,k}(z)=l_n(z,η_{nk}):k=0,...,n-1} for an appropriate choice of the parameters {η_{nk}:k=0,...,n-1} where l_n=k_{n+1}-k_n is the reproducing kernel for W_s. These observations form the basic ingredients for a wavelet type of analysis for orthogonal rational functions on the real line with respect to an arbitrary probability measure.
ISSN: 0163-0563
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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