On the uniqueness sets in the Fock space

Abstract

It was known to von Neumann in the 1950's that the integer lattice ${\mathbb{Z}}^2$ forms a uniqueness set for the Bargmann-Fock space. It was later demonstrated by Seip and Wallstén that a sequence of points $\Gamma$ that is uniformly close to the integer lattice is still a uniqueness set. We show in this paper that the uniqueness sets for the Fock space are preserved under much more general perturbations.