Density theorems for sampling and interpolation in the Bargmann-Fock space

Seip, Kristian

doi:10.1090/S0273-0979-1992-00290-2

Density theorems for sampling and interpolation in the Bargmann-Fock space
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Bull. Amer. Math. Soc. 26 (1992), 322-328 Request permission

Abstract:

We give a complete description of sampling and interpolation in the Bargmann-Fock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger than that of the von Neumann lattice, and similarly, a discrete set is a set of interpolation if and only if its density in every part of the plane is strictly smaller than that of the von Neumann lattice.

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