Projectable multivariate refinable functions and biorthogonal wavelets.
type: Item
instance of: scholarly article
title: Projectable multivariate refinable functions and biorthogonal wavelets.
zbMATH Open document ID: 1034.42036
DOI: 10.1016/S1063-5203(02)00007-6
author: Bin Han
published in: Applied and Computational Harmonic Analysis
publication date: 2003-04-02T00:00:00Z
review text: In the paper, the concept of projectable refinable functions is introduced, and it is shown that many non\-separable multivariate refinable functions in the literature are projectable, i.e., they essentially carry the tensor product structure. Projected refinable functions are constructed via a special class of linear transforms. Further, its analysis (smoothness, approximation order) is given. The theory can be used to tackle the following problem: Given a refinable function \(\phi \in {\mathbb R}^{^s}\), what are the expected optimal upper bounds of the \(L_p\)-smoothness and approximation order of all the dual refinable functions \(\phi^d\) of \(\phi \) such that the support of \(\phi^d\) is contained in a fixed set \([-N, N]^s\)?
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 68U07
zbMATH DE Number: 1891393
zbMATH Keywords: projectable refinable functions
zbMATH Keywords: projectable masks
zbMATH Keywords: biorthogonal wavelets
zbMATH Keywords: tensor product wavelets
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891393