Uniqueness of Fourier coefficients in L1
= Uniqueness of Fourier coefficients in L1
If a periodic integrable function has all <Fourier coefficients> zero, it vanishes almost everywhere. Its <Fejér sums> vanish, whereas the <Fejér kernel> is an approximate identity and converges to that function in the integrable norm. Applied to a periodized squared <Fourier transform>, this detects orthogonality of integer translates.