2 problems

Let $\mathcal{F}_\psi$ be the system of translates associated with a function $\psi$, and let $p_\psi$ be its periodization function on $\mathbb{T}$. Characterization conjecture. T…

Let $\mathcal{L}$ be a lattice and let $\mathcal{F}_\psi$ be the associated system of translates. A finite subset of $\mathcal{L}$ is an arithmetic progression when it has the form…