Fractal Interpolation over Nonlinear Partitions

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 funct...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Author: Massopust, Peter R
Format: Article
Language:English
Subjects:
Fractals
Function space
Interpolation
Partitions (mathematics)
Perturbation
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2203.07935