Fourier series and periodicity

TL;DR

This paper challenges the traditional view that periodicity is necessary for the pointwise convergence of Fourier series, showing that this condition can be relaxed.

Contribution

It demonstrates that the hypothesis of periodicity is not a necessary condition for the convergence of Fourier series.

Findings

Periodicity is not required for pointwise convergence.

Classical theorems on Fourier series can be generalized.

The paper provides new insights into Fourier analysis.

Abstract

A large number of the classical texts dealing with Fourier series more or less state that the hypothesis of periodicity is required for pointwise convergence. In this paper, we highlight the fact that this condition is not necessary.