Some topics on wavelet analysis
type: Item
instance of: scholarly article
title: Some topics on wavelet analysis
zbMATH Open document ID: 0815.42020
DOI: 10.1007/BF02661995
author: Daren Huang
author: Qiyu Sun
published in: Applied Mathematics. Series B (English Edition)
publication date: 1995-06-21T00:00:00Z
review text: This is a survey paper in which recent results in the following areas of wavelet analysis of functions in \(L^ p(\mathbb{R}^ d)\) are discussed: (1) the stability condition in the definition of a multiresolution analysis; (2) construction of wavelet bases (for \(p= 2\)); (3) use of the projection and quasi-interpolant to characterize Besov spaces and Triebel-Lizorkin spaces; (4) application of the Fourier method and the time domain method in the study of the ``refinement equation'' \(\varphi(n)= \sum a(n) \varphi(\alpha x- n)\), where \(a(0) a(N)\neq 0\) and \(\alpha> 1\), the sum is from \(n= 0\) to \(n= N\), and \(\varphi\) is a scaling function. There is a bibliography of 56 items, many from Chinese journals.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 468870
zbMATH Keywords: refinement equation
zbMATH Keywords: wavelet analysis
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: wavelet bases
zbMATH Keywords: Besov spaces
zbMATH Keywords: Triebel-Lizorkin spaces
zbMATH Keywords: scaling function
MaRDI profile type: Publication
cites work: On the construction of multivariate (pre)wavelets
cites work: Q4023039
cites work: Stationary subdivision
cites work: Q4003151
cites work: On Compactly Supported Spline Wavelets and a Duality Principle
cites work: A general framework of compactly supported splines and wavelets
cites work: Constructive function theory and spline systems
cites work: Biorthogonal bases of compactly supported wavelets
cites work: An Arithmetic Characterization of the Conjugate Quadrature Filters Associated to Orthonormal Wavelet Bases
cites work: Orthonormal bases of compactly supported wavelets
cites work: Two-Scale Difference Equations. I. Existence and Global Regularity of Solutions
cites work: Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
cites work: Q3983881
cites work: Image compression through wavelet transform coding
cites work: Compression of Wavelet Decompositions
cites work: Free multivariate splines
cites work: Interpolation through an iterative scheme
cites work: A discrete transform and decompositions of distribution spaces
cites work: Q3344703
cites work: Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
cites work: Necessary and sufficient conditions for constructing orthonormal wavelet bases
cites work: A theory for multiresolution signal decomposition: the wavelet representation
cites work: Q3784635
cites work: On the degree of nonlinear spline approximation in Besov-Sobolev spaces
cites work: Q4027550
cites work: Wavelets and pre-wavelets in low dimensions
cites work: A necessary and sufficient condition for the linear independence of the integer translates of a compactly supported distribution
cites work: Q3475804
cites work: Spline Representations of Functions in Besov-Triebel-Lizorkin Spaces on ℝ n
cites work: A remark on orthonormal bases of compactly supported wavelets in Triebel- Lizorkin spaces. The case \(0<p, q<\infty\)
cites work: Sequence spaces and stability of integer translates
cites work: Local approximation spaces
cites work: Q4025650
cites work: Q4031775
description: scientific article; zbMATH DE number 468870