Crystalline temperate distributions with uniformly discrete support and spectrum

Abstract

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).

References in corpus (3)

• Stable polynomials and crystalline measures
• Tempered distributions with discrete support and spectrum
• A Simple Crystalline Measure

Cited by in corpus (1)

• Taylor coefficients and zeroes of entire functions of exponential type