On the Fourier Representation of Computable Continuous Signals

Holger Boche; Ullrich J. Mönich

ICASSP 2019accepted0 citations

On the Fourier Representation of Computable Continuous Signals

Abstract

In this paper we study whether it is possible to decide algorithmically if the Fourier series of a continuous function converges uniformly. We show that this decision cannot be made algorithmically, because there exists no Turing machine that can decide for each and every continuous functions whether its Fourier series converges uniformly. Turing computability describes the theoretical feasible that can be implemented on a digital computer, hence the result shows that there exists no algorithm that can perform this decision.

BibTeX

@inproceedings{icassp2019_onthefourierrepr,
  title = {On the Fourier Representation of Computable Continuous Signals},
  author = {Holger Boche and Ullrich J. Mönich},
  booktitle = {ICASSP 2019},
  year = {2019}
}