Density theorems for sampling and interpolation in the Bargmann-Fock space
Complex Variables
2016-09-06 v1 Functional Analysis
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.
Cite
@article{arxiv.math/9204238,
title = {Density theorems for sampling and interpolation in the Bargmann-Fock space},
author = {Kristian Seip},
journal= {arXiv preprint arXiv:math/9204238},
year = {2016}
}
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7 pages