Dimension preserving approximation
S. Verma, Peter R. Massopust
TL;DR
This paper introduces the concept of dimension preserving approximation for continuous functions on [0,1], exploring how functions can be approximated while maintaining their fractal dimensions, and investigates related restrictions and extensions.
Contribution
It presents the first formal study of dimension preserving approximation and examines its implications for fractal dimension preservation in function restrictions and extensions.
Findings
Introduced the concept of dimension preserving approximation.
Analyzed restrictions and extensions of functions with respect to fractal dimensions.
Laid groundwork for future research in fractal dimension-preserving function approximation.
Abstract
This article introduces the novel notion of dimension preserving approximation for continuous functions defined on and initiates the study of it. Restrictions and extensions of continuous functions in regards to fractal dimensions are also investigated.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Approximation Theory and Sequence Spaces · Advanced Topology and Set Theory