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

Kristian Seip
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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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Kristian Seip. 1992-04-01. Density theorems for sampling and interpolation in the Bargmann-Fock space. https://arxiv.org/abs/math/9204238

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