Lp Solutions of Refinement Equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

23 Scopus Citations
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Author(s)

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Detail(s)

Original languageEnglish
Pages (from-to)143-167
Journal / PublicationJournal of Fourier Analysis and Applications
Volume7
Issue number2
Publication statusPublished - 2001

Abstract

In the recent characterizations of the Lp solution of the refinement equation in terms of the "p-norm joint spectral radius," there are problems in choosing the initial function for iteration [3, 23], or in addition, requiring stability of the refinable function [13,17]. In this article we overcome these difficulties and give a more complete characterization of this nature. The criterion is constructive and can be implemented. It can be used to describe the regularity of the solution without assuming stability. This has significant advantages over the previous work. The corresponding results for vector refinement equations are also discussed.

Research Area(s)

  • Joint spectral radii, Refinable functions, Refinement equations, Wavelets

Citation Format(s)

Lp Solutions of Refinement Equations. / Jia, Rong-Qing; Lau, Ka-Sing; Zhou, Ding-Xuan.

In: Journal of Fourier Analysis and Applications, Vol. 7, No. 2, 2001, p. 143-167.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review