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

preprint2016arXivOpen access

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.

Explore this paper’s authors, topics and related work.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Reviews 0

Write a reviewWrite

No reviews yet.

Discussion 0

Add a commentWrite

No comments yet.