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Chaos Solitons & Fractals
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Article . 2022
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Fractal Interpolation Over Nonlinear Partitions

Fractal interpolation over nonlinear partitions
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2022Embargo end date: 01 Jan 2022 English Publisher:Elsevier BVJournal:SSRN Electronic Journal (eissn: 1556-5068, Copyright policy )
Authors: Massopust, Peter R.;

doi: 10.2139/ssrn.4069644 , 10.1016/j.chaos.2022.112503 , 10.48550/arxiv.2203.07935

arXiv: 2203.07935

Fractal Interpolation Over Nonlinear Partitions

Abstract

This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation. In this context, perturbations of nonlinear partition functions are considered and sufficient conditions for the existence of a unique solution of the underlying fractal interpolation problem for some classes of function spaces are given.

Related Organizations
Keywords

Applications of operator theory to differential and integral equations, perturbation, Metric Geometry (math.MG), 28A80, 37L30, 46B25, 46E30, iterated function system, fractal interpolation, fractal function, Lebesgue-Bochner space, attractor, Fractals, Mathematics - Metric Geometry, Read-Bajraktarević operator, FOS: Mathematics, Interpolation in approximation theory

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    popularity
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Top 10%
Average
Top 10%
Green