Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic   and calculus
  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. 
Diederik Aerts, Marek Czachor, Maciej Kuna
math-ph math.MP nlin.CD quant-ph