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Density theorems for sampling and interpolation in the Bargmann-Fock space. II. (English) Zbl 0745.46033
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. The necessity of these conditions are proved in Part I (reviewed below) of the paper (by Seip), while this part deals with the sufficiency.
Reviewer: K.Seip

MSC:
46E15 Banach spaces of continuous, differentiable or analytic functions
41A05 Interpolation in approximation theory
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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