$\mathbf L^1$ completeness for Fourier series

TL;DR

This paper discusses how the Fubini theorem can be used to show that an $L^1$ function is uniquely determined by its Fourier coefficients, highlighting a theoretical aspect of Fourier analysis.

Contribution

It introduces a method leveraging Fubini's theorem to establish $L^1$ completeness for Fourier series, providing a new perspective on function determination.

Findings

$L^1$ functions are uniquely determined by their Fourier coefficients

Fubini theorem can be used to prove $L^1$ completeness

The approach offers a theoretical insight into Fourier analysis

Abstract

We note that the Fubini theorem may be used to prove that an $L^1$ function is determined by its Fourier coefficients.