Multivariate Gabor frames and sampling of entire functions of several variables

DOI10.1016/j.acha.2010.11.006zbMath1225.42022OpenAlexW2029170772MaRDI QIDQ550492

Karlheinz Gröchening

Publication date: 11 July 2011

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2010.11.006

zbMATH Keywords

latticeGauss functionGabor frameBargmann-Fock spaceentire functions of several variablesWeierstrass sigma-function

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Moment problems and interpolation problems in the complex plane (30E05) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items (11)

Smooth lattice orbits of nilpotent groups and strict comparison of projections ⋮ Completeness of coherent state subsystems for nilpotent Lie groups ⋮ Remarks on multivariate Gaussian Gabor frames ⋮ Gaussian Gabor frames, Seshadri constants and generalized Buser-Sarnak invariants ⋮ A geometric construction of tight multivariate Gabor frames with compactly supported smooth windows ⋮ Sampling of entire functions of several complex variables on a lattice and multivariate Gabor frames ⋮ The mystery of Gabor frames ⋮ Frame sequences and representations for samplable random processes ⋮ The canonical group of transformations of a Weyl-Heisenberg frame; applications to Gaussian and Hermitian frames ⋮ Dilation of the Weyl symbol and Balian-Low theorem ⋮ A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers

Cites Work

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• Remarks on multivariate Gaussian Gabor frames
• Banach spaces related to integrable group representations and their atomic decompositions. I
• Gabor (super)frames with Hermite functions
• Gabor representation of generalized functions
• Factoring polynomials with rational coefficients
• Describing functions: Atomic decompositions versus frames
• Interpolation with discrete sets in \(\mathbb{C}^ l\)
• Interpolation on plane sets in \({\mathbb{C}}^ 2\)
• Convergence and summability of Gabor expansions at the Nyquist density
• Interpolating varieties for weighted spaces of entire functions in \(\mathbb{C}^ n\)
• Gabor analysis and algorithms. Theory and applications
• Differentiation and the Balian-Low theorem
• Duality and biorthogonality for Weyl-Heisenberg frames
• Gabor time-frequency lattices and the Wexler-Raz identity
• Foundations of time-frequency analysis
• Hyperbolic secants yield Gabor frames
• Advances in Gabor analysis
• The Balian-Low theorem for symplectic lattices in higher dimensions
• Square integrable representations, von Neumann algebras and an application to Gabor 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
• Frames in the bargmann space of entire functions
• 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
• Varying the time-frequency lattice of Gabor frames
• Gabor Frames without Inequalities
• An introduction to frames and Riesz bases

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