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)...

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Classical Analysis and ODEs Functional Analysis 30D15, 42A38, 52C23