If X is a closed subset of the real line, denote by GX the supremum of the size of the gap in the Fourier spectrum of a measure, taken over all non-trivial finite complex measures supported on X. In this paper we attempt to find GX in terms of X.
"Spectral gaps for sets and measures." Acta Math. 208 (1) 151 - 209, 2012. https://doi.org/10.1007/s11511-012-0076-4