Intrinsic \(s\)-elementary Parseval frame multiwavelets in \(L^2(\mathbb R^d)\)
type: Item
instance of: scholarly article
title: Intrinsic \(s\)-elementary Parseval frame multiwavelets in \(L^2(\mathbb R^d)\)
zbMATH Open document ID: 1192.42023
author: Xingde Dai
author: Y. Diao
author: Zhongyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-05-10T00:00:00Z
review text: This paper studies some interesting theoretical properties of Parseval frame multiwavelets and addresses two problems on Parseval frame multiwavelets. Let \(A\) be a real expansive dilation matrix and \(m\) be a positive integer. Theorem 3.4 shows that there always exists an intrinsic \(A\)-dilation Parseval frame multiwavelet set with length \(m\) (see Definition 1.1). Theorem 4.1 proves that the set of all \(A\)-dilation s-elementary Parseval frame multiwavelets of length \(m\) is path-connected and Theorem 4.5 demonstrates that the set of all intrinsic \(A\)-dilation s-elementary Parseval frame multiwavelets of length \(m\) is path-connected. Furthermore, a generalized result in Theorem 5.2 shows that there exist intrinsic \(A\)-dilation Parseval frame multiwavelets of length \(m\).
reviewed by: Bin Han
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5706233
zbMATH Keywords: Multiwavelets
zbMATH Keywords: Parseval frames
zbMATH Keywords: s-elementary Parseval frame multiwavelets
zbMATH Keywords: Path-connectivity
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.02.016
OpenAlex ID: W1978595356
cites work: Compactly supported tight and sibling frames with maximum vanishing moments
cites work: The wavelet transform, time-frequency localization and signal analysis
cites work: Ten Lectures on Wavelets
cites work: Pairs of dual wavelet frames from any two refinable functions
cites work: Framelets: MRA-based constructions of wavelet frames
cites work: Frames, bases and group representations
cites work: Dual multiwavelet frames with high balancing order and compact fast frame transform
cites work: ANALYSIS OF THE STRONG INSTANCE FOR THE VECTOR DECOMPOSITION PROBLEM
cites work: Riesz multiwavelet bases generated by vector refinement equation
cites work: Wandering vectors for unitary systems and orthogonal wavelets
cites work: The s-elementary frame wavelets are path connected
cites work: Tight frame wavelets, their dimension functions, MRA tight frame wavelets and connectivity properties
cites work: The s-elementary wavelets are path-connected
cites work: Basic properties of wavelets
cites work: Wavelet sets in \(\mathbb{R}^ n\)
cites work: The path-connectivity of MRA wavelets in \(L^2(\mathbb R^d)\)
cites work: Multipliers, phases and connectivity of MRA wavelets in \(L^{2}(\mathbb R^{2})\)
cites work: Frame wavelet sets in \(\mathbb{R}\)
cites work: Some equations relating multiwavelets and multiscaling functions
cites work: Frame wavelets in subspaces of $L^2(\mathbb R^d)$
cites work: On multiresolution analysis (MRA) wavelets in \(\mathbb{R}^n\)
cites work: Wavelets in subspaces
DOI: 10.1016/J.JMAA.2010.02.016
description: scientific article; zbMATH DE number 5706233