Density theorems for sampling and interpolation \\ in the Bargmann-Fock space
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Publication:4005823
DOI10.1090/S0273-0979-1992-00290-2zbMath0808.30019arXivmath/9204238MaRDI QIDQ4005823
Publication date: 27 September 1992
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/9204238
Coherent states (81R30) Moment problems and interpolation problems in the complex plane (30E05) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Representations of entire functions of one complex variable by series and integrals (30D10)
Related Items (19)
Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions ⋮ Gabor frame sets of invariance: a Hamiltonian approach to Gabor frame deformations ⋮ Multiple sampling and interpolation in weighted Fock spaces of entire functions ⋮ Sampling in the image of Sobolev space in \(L^2(\mathbb{R}, e^{u^2}du)\) under Schrödinger semigroup \(e^{it\Delta } \) ⋮ Determinantal processes and completeness of random exponentials: the critical case ⋮ Beurling-type density criteria for system identification ⋮ Sampling measure on doubling Fock spaces ⋮ A stability problem for some complete and minimal Gabor systems in $L^2(\mathbb {R})$ ⋮ Minimal frame operator norms via minimal theta functions ⋮ The Mittag Leffler reproducing kernel Hilbert spaces of entire and analytic functions ⋮ Some curious results related to a conjecture of Strohmer and Beaver ⋮ Identification of stochastic operators ⋮ Gaussian distributions and phase space Weyl-Heisenberg frames ⋮ On zero sets in Fock spaces ⋮ Duality for frames ⋮ Riesz bases of reproducing kernels in small Fock spaces ⋮ On the parity under metapletic operators and an extension of a result of Lyubarskii and Nes ⋮ Complete interpolating sequences for small Fock spaces ⋮ Necessary density conditions for \(d\)-approximate interpolation sequences in the Bargmann-Fock space
Cites Work
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- Hankel forms and the Fock space
- The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer
- Beurling type density theorems in the unit disk
- A Riesz basis for Bargmann-Fock space related to sampling and interpolation
- Necessary density conditions for sampling an interpolation of certain entire functions
- Painless nonorthogonal expansions
- Frames in the bargmann space of entire functions
- Reproducing Formulas and Double Orthogonality in Bargmann and Bergman Spaces
- The wavelet transform, time-frequency localization and signal analysis
- Harmonic Analysis in Phase Space. (AM-122)
- Density theorems for sampling and interpolation in the Bargmann-Fock space I.
- Regular Sets of Sampling and Interpolation for Weighted Bergman Spaces
- A Class of Nonharmonic Fourier Series
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