Crystalline temperate distributions with uniformly discrete support and spectrum

11 Jan 2021 · Nir Lev, Gilad Reti ·

We prove that a temperate distribution on $\mathbb{R}$ whose support and spectrum are uniformly discrete sets, can be obtained from Poisson's summation formula by a finite number of basic operations (shifts, modulations, differentiations, multiplication by polynomials, and taking linear combinations).