Density theorems for sampling and interpolation in the Bargmann-Fock space I.
Copyright policy )Density theorems for sampling and interpolation in the Bargmann-Fock space I.
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.
7 pages
- DigiZeitschriften Germany
Representations of entire functions of one complex variable by series and integrals, Mathematics - Complex Variables, sampling and interpolation in the Bargmann-Fock space, Moment problems and interpolation problems in the complex plane, Article, density concept of Beurling, Functional Analysis (math.FA), Mathematics - Functional Analysis, 510.mathematics, necessity, von Neumann lattice, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, Banach spaces of continuous, differentiable or analytic functions, Bargmann-Fock spaces, FOS: Mathematics, Coherent states, Complex Variables (math.CV), Hilbert spaces of continuous, differentiable or analytic functions, Interpolation in approximation theory
Representations of entire functions of one complex variable by series and integrals, Mathematics - Complex Variables, sampling and interpolation in the Bargmann-Fock space, Moment problems and interpolation problems in the complex plane, Article, density concept of Beurling, Functional Analysis (math.FA), Mathematics - Functional Analysis, 510.mathematics, necessity, von Neumann lattice, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, Banach spaces of continuous, differentiable or analytic functions, Bargmann-Fock spaces, FOS: Mathematics, Coherent states, Complex Variables (math.CV), Hilbert spaces of continuous, differentiable or analytic functions, Interpolation in approximation theory
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