3 problems

Let $\mu$ be a tempered distribution such that both $\mu$ and its Fourier transform $\widehat\mu$ are pure-point Radon measures of locally finite support; such a distribution is ca…

Let $\mu$ be a crystalline measure on $\mathbb R^n$ with support $\Lambda$ and spectrum $S$. A set is relatively uniformly discrete if it is a finite union of uniformly discrete se…

Lagarias's conjecture. If $\Lambda$ and $S$ are uniformly discrete, then $\mu$ is trivial and all the lattices $L_j$ are equal. The conjecture is known when $n=1$ or when $\mu$ is…