Fourier Quasicrystals and Distributions on Euclidean Spaces with Spectrum of Bounded Density

Abstract

We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sums of derivatives of generalized lattice Dirac combs. These theorems are derived from properties of families of discretely supported measures and almost periodic distributions.