Analytic wavelets generated by radial functions
type: Item
instance of: scholarly article
title: Analytic wavelets generated by radial functions
zbMATH Open document ID: 0855.65145
DOI: 10.1007/BF02124736
published in: Advances in Computational Mathematics
publication date: 1997-02-11T00:00:00Z
review text: The paper deals with a class of non-stationary multiresolution analysis and wavelets generated by radial basis functions. The multiresolution analysis is generated by \(\phi \in L^2(\mathbb{R}^d)\) by letting \[ V_j := \text{clos}_{L^2} \text{span} \{\phi (\cdot - A^{-j}k), \quad k \in\mathbb{Z}\}, \] where \(A\) is a \(d \times d\) integer matrix, and all eigenvalues of \(A\) have absolute value \(> 1\). Note that no dilation of \(\phi\) appears in the definition of \(V_j\). The Littlewood-Paley identity is proved, and time and frequency localization of the corresponding wavelet basis are studied. Examples are based on multiquadric wavelets.
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 892179
zbMATH Keywords: analytic wavelets
zbMATH Keywords: time-frequency window
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: radial basis functions
zbMATH Keywords: Littlewood-Paley identity
zbMATH Keywords: multiquadric wavelets
author: Charles K. Chui
author: Joachim Stöckler
author: J. D. Ward
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 892179