Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
Mathematical Physics
2016-07-26 v1 math.MP
Chaotic Dynamics
Quantum Physics
Abstract
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the expected 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
Cite
@article{arxiv.1603.05471,
title = {Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus},
author = {Diederik Aerts and Marek Czachor and Maciej Kuna},
journal= {arXiv preprint arXiv:1603.05471},
year = {2016}
}