Rajchman measure

Summary

A Rajchman measure is a finite measure on a locally compact abelian group whose Fourier–Stieltjes transform tends to zero at infinity. On the circle, this means that the Fourier coefficients $\hat\mu(n)$ tend to $0$ as $\abs{n} \to \infty$. Every absolutely continuous measure is Rajchman by the Riemann–Lebesgue lemma, but some singular measures are Rajchman too. These measures are central in the study of sets of uniqueness and multiplicity for trigonometric series.