Homogeneous approximation property for wavelet frames with matrix dilations. II.
type: Item
instance of: scholarly article
title: Homogeneous approximation property for wavelet frames with matrix dilations. II.
zbMATH Open document ID: 1267.42037
author: Zhi Jing Zhao
author: Wenchang Sun
publication date: 2013-03-19T00:00:00Z
review text: The authors' study is the homogeneous approximation property, which states that the number of building blocks in a reconstruction of a function up to some error is essentially invariant under time-scale shifts and give conditions on a wavelet function, both in terms of its Fourier transform and the values of the wavelet itself, so that the corresponding wavelet frame with an arbitrary expansive dilation matrix has the homogeneous approximation property. For Part I see [\textit{W. Sun}, Math. Nachr. 283, No. 10, 1488--1505 (2010; Zbl 1201.42027)].
reviewed by: Gustaf Gripenberg
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 6146296
zbMATH Keywords: wavelet frames
zbMATH Keywords: homogeneous approximation property
zbMATH Keywords: matrix dilations
MaRDI profile type: Publication
full work available at URL: s10114-012-0546-9
OpenAlex ID: W2033795943
cites work: An introduction to frames and Riesz bases
cites work: Q3955832
cites work: Density, overcompleteness, and localization of frames. I: Theory
cites work: Compactly supported tight and sibling frames with maximum vanishing moments
cites work: Inequalities of Littlewood–Paley Type for Frames and Wavelets
cites work: Orthonormal wavelets and tight frames with arbitrary real dilations
cites work: Ten Lectures on Wavelets
cites work: Framelets: MRA-based constructions of wavelet frames
cites work: Localization of frames, Banach frames, and the invertibility of the frame operator
cites work: Localized frames are finite unions of Riesz sequences
cites work: Continuous and Discrete Wavelet Transforms
cites work: Affine systems in \(L_ 2(\mathbb{R}^d)\): The analysis of the analysis operator
cites work: Generalized shift-invariant systems
cites work: Wiener’s lemma for infinite matrices
cites work: The Homogeneous Approximation Property and the Comparison Theorem for Coherent Frames
cites work: The homogeneous approximation property for wavelet frames
cites work: Affine density in wavelet analysis
cites work: Homogeneous approximation property for wavelet frames
cites work: Homogeneous approximation property for wavelet frames with matrix dilations
DOI: 10.1007/S10114-012-0546-9
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6146296