Self-affine fractal functions and wavelet series
type: Item
instance of: scholarly article
title: Self-affine fractal functions and wavelet series
zbMATH Open document ID: 0946.28005
author: Peter Singer
author: Peter Zajdler
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-10-18T00:00:00Z
review text: The authors study functions represented by series of wavelet-type: \[ f(x) = \sum_{g \in G} c_g \psi(g^{-1}(x)), \] where \(G\) is a group generated by affine functions \(L_1, \ldots, L_n\) and \(\psi\) is piecewise affine. They show that the class of self-affine fractal functions previously studied by \textit{M. F. Barnsley} and \textit{S. Demko} [Proc. R. Soc. Lond., Ser. A 399, 243-275 (1985; Zbl 0588.28002)] and \textit{M. F. Barnsley} [Constructive Approximation 2, 303-329 (1986; Zbl 0606.41005)] and classical fractal functions such as Devil's Staircase of Cantor-Lebesgue and Weierstrass-like nowhere differentiable functions can be characterized by such series. As applications, the authors compute the global and local Hölder exponents of affine wavelet-type functions, and they also construct functions with prescribed local Hölder exponents at each point.
reviewed by: Y. Xiao
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 37C45
zbMATH DE Number: 1417580
zbMATH Keywords: fractals
zbMATH Keywords: wavelets
zbMATH Keywords: functional equations
zbMATH Keywords: Hölder exponents
MaRDI profile type: Publication
OpenAlex ID: W2020053085
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DOI: 10.1006/JMAA.1999.6614
description: scientific article; zbMATH DE number 1417580