Critical and asymmetric Fourier uniqueness pairs

Abstract: Motivated by the recent work of Kulikov, Nazarov, and Sodin, we construct a sufficient condition for discrete subsets of $\mathbb{R}$, which lie between the supercritical and subcritical cases, to constitute Fourier uniqueness pairs. This family of critical uniqueness pairs includes pairs that are strongly asymmetric, stretching beyond those associated with zeros of zeta and L-functions, discovered by Bondarenko, Radchenko, and Seip, and getting close to the classical Shannon--Whittaker uniqueness pair.