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 can...Show MoreMetadata
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.
Published in: ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Date of Conference: 12-17 May 2019
Date Added to IEEE Xplore: 17 April 2019
ISBN Information: