On the relationships between Fourier–Stieltjes coefficients and spectra of measures
Volume 221 / 2014
Studia Mathematica 221 (2014), 117-140
MSC: Primary 43A10; Secondary 43A25.
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 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.
