Determining sets of frequencies in spectra of measures with finite energy

A set, is said to be determining if for any measure on the circumference such that one has the inequality, in the paper one shows that the upper density of any determining set is positive. On the other hand, there exist subsets of the set+ having arbitrarily small density.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 107, pp. 222–227, 1982.