The smoothness and dimension of fractal interpolation functions
type: Item
instance of: scholarly article
title: The smoothness and dimension of fractal interpolation functions
zbMATH Open document ID: 0878.41016
DOI: 10.1007/BF02662880
author: Gang Chen
published in: Applied Mathematics. Series B (English Edition)
publication date: 1997-12-15T00:00:00Z
review text: \textit{M. F. Barnsley}, Constructive Approximation 2, 303-329 (1986; Zbl 0606.41005), introduced so-called fractal interpolation of a function defined in \([0,1]\) on nodes \(0 =x_0 <x_1 <\cdots <x_n =1\) by a continuous function \(f\) whose graph is the unique attractor of a certain iterated function system. The author considers a special class of such iterated function systems whose construction involves \(n\) auxiliary functions \(q_i\) as well as other parameters. Extending and in some cases improving the results of \textit{Z. Sha} and \textit{G. Chen}, Approximation Theory Appl. 9, No. 4, 73-88 (1993; Zbl 0784.41001), he obtains various statements about the smoothness of \(f\) when \(q_i\in \text{Lip} \alpha\) and under suitable assumptions on the other parameters. He also discusses series expansions involving the interpolation functions as well as giving box counting dimension estimates for the graph of \(f\) in a critical case.
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 976120
reviewed by: I. N. Baker
MaRDI profile type: Publication
cites work: Fractal functions and interpolation
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full work available at URL: https://doi.org/10.1007/bf02662880
OpenAlex ID: W87078738
description: scientific article; zbMATH DE number 976120