On the relationships between Fourier-Stieltjes coefficients and spectra of measures
Przemysław Ohrysko, Michał Wojciechowski (2014)
Studia Mathematica
Similarity:
We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group with Fourier coefficients taking values in this set has a natural spectrum. For measures with Fourier coefficients tending to 0 we construct an open set with this property. We also give an example of a singular measure whose spectrum is contained in our set.