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 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.

References in corpus (2)

• Introduction to Projective Arithmetics
• New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems

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