Fourier uniqueness and non-uniqueness pairs
Aleksei Kulikov, Федор Леонидович Назаров, Mikhail Sodin · arXiv (Cornell University) · 2023
Motivated by recent works by Radchenko and Viazovska and by Ramos and Sousa, we find sufficient conditions for a pair of discrete subsets of the real line to be a uniqueness or a non-uniqueness pair for the Fourier transform. These conditions are close to each other. The uniqueness result can be upgraded to an interpolation formula, which in turn produces an abundance of discrete measures with discrete Fourier transform.