On the relationships between Fourier - Stieltjes coefficients and spectra of measures
arXiv:1305.3324 · doi:10.4064/sm221-2-2
Abstract
We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group taking values of its Fourier coefficients from this set has natural spectrum. For measures with Fourier coefficients tending to 0 we construct tho open set with this property.
28 pages