Fractal interpolation surfaces and a related 2-D multiresolution analysis
type: Item
instance of: scholarly article
title: Fractal interpolation surfaces and a related 2-D multiresolution analysis
zbMATH Open document ID: 0778.65009
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-09-05T00:00:00Z
review text: The concept of self-affine fractal interpolation surfaces which was given by \textit{P. R. Massopust} [J. Math. Anal. Appl. 151, No. 1, 275-290 (1990; Zbl 0716.28007)] for triangular domains, is extended to polygonal domains and arbitrary interpolation points. The concept uses so called fractal interpolation functions. An algorithm is described. A class of invariant measures supported on these surfaces is introduced and discussed as well as the fractal dimension of some simple surfaces. Using these surfaces the authors construct a sequence of nested subspaces forming a generalized multiresolution analysis.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 399085
zbMATH Keywords: self-affine fractal interpolation surfaces
zbMATH Keywords: polygonal domains
zbMATH Keywords: fractal interpolation functions
zbMATH Keywords: algorithm
zbMATH Keywords: invariant measures
zbMATH Keywords: fractal dimension
zbMATH Keywords: multiresolution analysis
author: Jeffrey S. Geronimo
author: D. P. Hardin
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1232
OpenAlex ID: W2071416197
DOI: 10.1006/JMAA.1993.1232
description: scientific article; zbMATH DE number 399085