Description
We give definitions of crystalline measure and Fourier quasicrystal, discuss the relationship between these notions, and show some sufficient conditions for a crystalline measure to be a Fourier quasicrystal. We then present the theorem of Olevskii and Ulanovskii on the 1-1 correspondence between zeros of exponential polynomials and Fourier quasicrystals with unit masses. We show generalizations of this result to the zeros of absolutely convergence Dirichlet series, to slowly growing measures with countable spectrum, to the zeros of almost periodic functions in a strip. The last result yields the simple criterion of representability of almost periodic entire functions of exponential growth (in particular exponential polynomials) as a finite product of sines.