@inproceedings{8f4beed1428548e2a3ff22641296f29f,
title = "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.",
keywords = "Fourier series, Turing computability, continuous function, uniform convergence",
author = "Holger Boche and Monich, {Ullrich J.}",
note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 ; Conference date: 12-05-2019 Through 17-05-2019",
year = "2019",
month = may,
doi = "10.1109/ICASSP.2019.8683074",
language = "English",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "5013--5017",
booktitle = "2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings",
}