Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

Diederik Aerts (), Marek Czachor and Maciej Kuna

Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 461-468

Abstract: Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

Keywords: Fourier transform; Cantor set; Arithmetic (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:91:y:2016:i:c:p:461-468

DOI: 10.1016/j.chaos.2016.07.008

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