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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

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


Author: Kristian Seip
Journal: Bull. Amer. Math. Soc. 26 (1992), 322-328
MSC (2000): Primary 30D15; Secondary 46E22
DOI: https://doi.org/10.1090/S0273-0979-1992-00290-2
MathSciNet review: 1136138
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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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DOI: https://doi.org/10.1090/S0273-0979-1992-00290-2
Article copyright: © Copyright 1992 American Mathematical Society