Sampling of entire functions of several complex variables on a lattice and multivariate Gabor frames

DOI10.1080/17476933.2019.1681415zbMath1451.42040arXiv1905.09927OpenAlexW2982487591WikidataQ126858798 ScholiaQ126858798MaRDI QIDQ5132205

Yurij I. Lyubarskij, Karlheinz Gröchening

Publication date: 10 November 2020

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.09927

zbMATH Keywords

latticeGauss functionGabor frameentire functions of several variablesWeierstrass sigma functioninterpolating function

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Applications of hypergeometric functions (33C90) Other generalizations of function theory of one complex variable (32A30)

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Gaussian Gabor frames, Seshadri constants and generalized Buser-Sarnak invariants ⋮ The mystery of Gabor frames ⋮ Sampling in spaces of entire functions of exponential type in \(\mathbb{C}^{n + 1} \) ⋮ A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers

Cites Work

• Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions
• Remarks on multivariate Gaussian Gabor frames
• The mystery of Gabor frames
• Multivariate Gabor frames and sampling of entire functions of several variables
• Banach spaces related to integrable group representations and their atomic decompositions. I
• Factoring polynomials with rational coefficients
• Interpolation with discrete sets in \(\mathbb{C}^ l\)
• Beurling-type density theorems for weighted \(L^p\) spaces of entire functions
• Weyl-Heisenberg frames and Riesz bases in \(L_2(\mathbb{R}^d)\)
• Duality and biorthogonality for Weyl-Heisenberg frames
• Complete interpolating sequences for Fourier transforms supported by convex symmetric pol\-y\-gons
• Foundations of time-frequency analysis
• History and evolution of the density theorem for Gabor frames
• On a Hilbert space of analytic functions and an associated integral transform part I
• Basic Complex Analysis
• Harmonic Analysis in Phase Space. (AM-122)
• Density theorems for sampling and interpolation in the Bargmann-Fock space I.
• The Local Growth of Power Series: A Survey of the Wiman-Valiron Method
• Gabor Frames without Inequalities
• Interpolating sequences for Bargmann-Fock spaces in \(\mathbb C^n\)
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