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

Diederik Aerts; Marek Czachor; Maciej Kuna

doi:10.1016/j.chaos.2016.07.008

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

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.

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Authors (3)

Diederik Aerts
- Vrije Universiteit Brussel, Bruksela, Belgia Centrum Leo Apostel
Marek Czachor prof. dr hab.
Maciej Kuna dr

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DOI:: Digital Object Identifier (open in new tab) 10.1016/j.chaos.2016.07.008
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Details

Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: CHAOS SOLITONS & FRACTALS no. 91, pages 461 - 468,
ISSN: 0960-0779
Language:: English
Publication year:: 2016
Bibliographic description:: Aerts, D., Czachor M., Kuna M.: Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus// CHAOS SOLITONS & FRACTALS. -Vol. 91, (2016), s.461-468
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.chaos.2016.07.008
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