Biorthogonal two-direction refinable function and two-direction wavelet
type: Item
instance of: scholarly article
title: Biorthogonal two-direction refinable function and two-direction wavelet
zbMATH Open document ID: 1108.65130
author: S. Z. Yang
published in: Applied Mathematics and Computation
publication date: 2007-01-11T00:00:00Z
review text: The author generalizes the theory of refinable functions and biorthogonal wavelets. He considers a so-called two-direction refinable function \(\varphi \in L^2({\mathbb R})\) which satisfies \[ \varphi(x)=\sum_{k=-\infty}^{\infty}\big(p_k^{+}\, \varphi(2x-k) + p_k^{-}\,\varphi(k-2x)\big) \] with 2 masks \(\{p_k^{\pm}\}\in l^2({\mathbb Z})\). The properties of the positive/negative-direction symbols are studied. Using these symbols, biorthogonal two-direction refinable functions and corresponding biorthogonal two-direction wavelets are characterized. Finally, two examples illustrate the construction of biorthogonal two-direction wavelets.
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5115442
zbMATH Keywords: refinable function
zbMATH Keywords: two-direction refinable function
zbMATH Keywords: wavelet
zbMATH Keywords: biorthogonal two-direction wavelets
zbMATH Keywords: symbols
zbMATH Keywords: numerical examples
reviewed by: Manfred Tasche
MaRDI profile type: Publication
full work available at URL: j.amc.2006.06.003
OpenAlex ID: W1991526800
cites work: Ten Lectures on Wavelets
cites work: Orthonormal bases of compactly supported wavelets
cites work: On Compactly Supported Spline Wavelets and a Duality Principle
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: On existence and weak stability of matrix refinable functions
cites work: Q3839129
cites work: Fractal functions and wavelet expansions based on several scaling functions
cites work: Construction of biorthogonal multiwavelets
cites work: A fast algorithm for constructing orthogonal multiwavelets
cites work: Raising approximation order of refinable vector by increasing multiplicity
cites work: Refinable Function Vectors
cites work: A study of orthonormal multi-wavelets
cites work: Orthogonality criteria for multi-scaling functions
cites work: High-order balanced multiwavelets: theory, factorization, and design
cites work: On a family of orthonormal scalar wavelets and related balanced multiwavelets
DOI: 10.1016/J.AMC.2006.06.003
description: scientific article; zbMATH DE number 5115442