Accuracy of multivariable refinable functions and two-scale similarity transform
type: Item
instance of: scholarly article
title: Accuracy of multivariable refinable functions and two-scale similarity transform
zbMATH Open document ID: 0980.42034
author: Silong Peng
author: Qiuhui Sheng
publication date: 2002-02-19T00:00:00Z
review text: The paper considers refinable function vectors \(\Phi\) with dilation matrix \(M=\text{diag}(2,2,\dots, 2)\). Let \(m(\xi)\) be a refinement symbol of the refinable vector \(\pmb\Phi\) and let \(\Phi\) provide accuracy \(p\). Then, under some additional conditions, the vector \(\pmb\Psi\) with refinement symbol \[ \tilde m(\xi)=T( 2\xi)^{-1}m(\xi)T(\xi) \] also provides accuracy \(p\), if \(T(\xi)\) is a \(2\pi\)-periodic, invertible matrix, i.e., the so-called two-scale similarity transform keeps the accuracy.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 1501752
zbMATH Keywords: accuracy
zbMATH Keywords: refinable function vectors
zbMATH Keywords: two-scale similarity transform
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
full work available at URL: s101140050007
OpenAlex ID: W4254031447
cites work: Approximation by translates of refinable functions
cites work: Approximation order provided by refinable function vectors
cites work: Accuracy of lattice translates of several multidimensional refinable functions
cites work: Q4778419
cites work: Q4890498
DOI: 10.1007/S101140050007
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1501752