\(M\)-band scaling function with filter having vanishing moments two and minimal length
type: Item
instance of: scholarly article
title: \(M\)-band scaling function with filter having vanishing moments two and minimal length
zbMATH Open document ID: 0938.42022
author: Qiyu Sun
author: Zeyin Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-01-24T00:00:00Z
review text: In this paper, the authors consider the Hölder continuity, local linearity, linear independence and interpolation problem for the \(M\)-band scaling functions with two vanishing moments and minimal length. Thus the \(M\)-band filter transfer function is factorized as \(H(z)=({{1-z^M}\over {M(1-z)}})^2(\alpha+\beta z)z^k\). The scaling function \(\phi_M\) is obtained from the usual refinement equation \({\widehat{\phi}}(z)=H({{z}\over{M}}) {\widehat{\phi}}({{z}\over{M}})\). In particular, the authors obtain that \(\phi_M\) is locally linear on an open set with full measure and locally dependent when \(M\geq 3\); \(\widetilde{\phi}_M\) is differentiable at \(M\)-adic points when \(M=3\), and \(\widetilde{\phi}_M\) is not interpolatable at \(Z\) when \(M=11\), where \(\widetilde{\phi}_M(x) = \phi(2+1/(M-1)-x)\).
reviewed by: Radu Balan
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1217011
zbMATH Keywords: \(M\)-band scaling function
zbMATH Keywords: interpolation problem
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5936
OpenAlex ID: W2074003517
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DOI: 10.1006/JMAA.1998.5936
description: scientific article; zbMATH DE number 1217011