Multiresolution analyses based on fractal functions
type: Item
instance of: scholarly article
title: Multiresolution analyses based on fractal functions
zbMATH Open document ID: 0772.41002
DOI: 10.1016/0021-9045(92)90134-A
author: D. P. Hardin
author: Bruce Kessler
author: Peter Massopust
published in: Journal of Approximation Theory
publication date: 1993-01-16T00:00:00Z
review text: The aim of this paper is to construct multiresolution analyses (see the paper for the definition) based on fractal interpolation functions (FIF). The use of finite sets of such functions is motivated by the fact that they are self-affine, i.e. each FIF is a finite union of affine imagines of itself and has non-integral dimension \(d\), which can be used as an additional parameter in characterizing highly complex sets. They obey to a dilation equation and FIF theory is related also to wavelet theory. Section 3 is concerned with multiresolution analyses in \(L^ 2(\mathbb{R})\) and \(C_ 0(\mathbb{R})\). Section 4 is devoted to explicit constructions of the set that generates the multiresolution analyses and with application to decomposition and reconstruction algorithms to concrete examples, namely in \(V_ k\cap L^ 2(\mathbb{R})\) and \(V_ k\cap C_ 0(\mathbb{R})\), where \(\{V_ k\}_{k\geq 0}\) is a nested sequence of linear subspaces considered in Section 3. The examples are illustrated on some figures.
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 93298
zbMATH Keywords: fractal interpolation functions
zbMATH Keywords: wavelet theory
zbMATH Keywords: multiresolution analyses
zbMATH Keywords: reconstruction algorithms
reviewed by: Costică Mustăţa
MaRDI profile type: Publication
cites work: Fractal functions and interpolation
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cites work: Q3731958
cites work: Orthonormal bases of compactly supported wavelets
cites work: Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
cites work: Q3784635
full work available at URL: 0021-9045(92)90134-a
OpenAlex ID: W1963684587
description: scientific article; zbMATH DE number 93298