Internal structure of the multiresolution analyses defined by the unitary extension principle
type: Item
instance of: scholarly article
title: Internal structure of the multiresolution analyses defined by the unitary extension principle
zbMATH Open document ID: 1161.42019
author: Hong Oh Kim
author: Rae Young Kim
author: Jae Kun Lim
published in: Journal of Approximation Theory
publication date: 2009-02-03T00:00:00Z
review text: This paper investigates the internal structure of the multiresolution analysis of \(L^2(\mathbb{R}^d)\) associated with a wavelet tight frame constructed by the unitary extension principle. Let \(V_0\) denote the closed linear span of the integer shifts of the scaling refinable function and \(V_1\) be the dyadic dilation of \(V_0\). Let \(W_0\) denote the closed linear span of the integer shifts of all the wavelet functions. This paper characterizes the conditions such that \(V_1=W_0\), \(V_1\) is the sum of \(V_0\) and \(W_0\), and \(V_1\) is a direct sum of \(V_0\) and \(W_0\), respectively. A more detailed analysis for trigonometric filters is also provided.
reviewed by: Bin Han
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5501952
zbMATH Keywords: Multiresolution analysis
zbMATH Keywords: tight wavelet frames
zbMATH Keywords: shift-invariant space
zbMATH Keywords: unitary extension principle
MaRDI profile type: Publication
full work available at URL: j.jat.2008.03.009
OpenAlex ID: W2019359984
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DOI: 10.1016/J.JAT.2008.03.009
description: scientific article; zbMATH DE number 5501952