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Local Fractal Interpolation on Unbounded Domains

Part of: Smooth dynamical systems: general theory Harmonic analysis in several variables Classical measure theory Approximations and expansions

Published online by Cambridge University Press:  23 January 2018

Peter R. Massopust
Peter R. Massopust*
Affiliation:
Centre of Mathematics, Research Unit M15, Technische Universität München, Boltzmannstrasse 3, 85747 Garching b. München, Germany (massopust@ma.tum.de)
*
Corresponding author.
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Abstract

We define fractal interpolation on unbounded domains for a certain class of topological spaces and construct local fractal functions. In addition, we derive some properties of these local fractal functions, consider their tensor products, and give conditions for local fractal functions on unbounded domains to be elements of Bochner–Lebesgue spaces.

Keywords

local iterated function systemattractorfractal interpolationRead–Bajraktarević operatorfractal functionBochner–Lebesgue spaceunbounded componentnon-compact Hausdorff space

MSC classification

Primary: 28A80: Fractals 37C70: Attractors and repellers, topological structure 41A05: Interpolation 41A30: Approximation by other special function classes 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 1 , February 2018 , pp. 151 - 167
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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