Banach Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group

DOI10.1080/00036811.2011.584186zbMath1266.46020arXiv1012.4283OpenAlexW2601098156WikidataQ58243588 ScholiaQ58243588MaRDI QIDQ4650230

Karlheinz Gröchening, Luís Daniel Abreu

Publication date: 27 November 2012

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.4283

zbMATH Keywords

Heisenberg groupGabor framesHermite functionsFock spacepolyanalytic functionscoorbit theory

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General harmonic expansions, frames (42C15) Interpolation in approximation theory (41A05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Banach spaces of continuous, differentiable or analytic functions (46E15) Bergman spaces and Fock spaces (30H20)

Related Items (28)

Berezin-Toeplitz quantization associated with higher Landau levels of the Bochner Laplacian ⋮ Intermediate Hankel operators on the Fock space ⋮ On the structure of polyharmonic Bergman-type spaces over the unit disk ⋮ On Toeplitz operators and localization operators ⋮ Density of polyanalytic polynomials in complex and quaternionic polyanalytic weighted Bergman spaces ⋮ Harmonic analysis in phase space and finite Weyl-Heisenberg ensembles ⋮ Gabor products and a phase space approach to nonlinear analysis ⋮ Density of complex and quaternionic polyanalytic polynomials in polyanalytic Fock spaces ⋮ Approximation by convolution polyanalytic operators in the complex and quaternionic compact unit balls ⋮ On the representation and the uniform polynomial approximation of polyanalytic functions of Gevrey type on the unit disk ⋮ Frames adapted to a phase-space cover ⋮ Polyharmonic Bergman spaces and Bargmann type transforms ⋮ The canonical group of transformations of a Weyl-Heisenberg frame; applications to Gaussian and Hermitian frames ⋮ Structural results for quaternionic Gabor frames ⋮ Superframes and polyanalytic wavelets ⋮ Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator ⋮ Super-wavelets versus poly-Bergman spaces ⋮ What is the Wigner Function Closest to a Given Square Integrable Function? ⋮ Planar sampling sets for the short-time Fourier transform ⋮ Polyanalytic Toeplitz operators: isomorphisms, symbolic calculus and approximation of Weyl operators ⋮ Donoho-Logan large sieve principles for modulation and polyanalytic Fock spaces ⋮ Nonlinear coherent states associated with a measure on the positive real half line ⋮ Reproducing kernel Hilbert spaces of CR functions for the Euclidean motion group ⋮ Designing Gabor windows using convex optimization ⋮ Sampling trajectories for the short-time Fourier transform ⋮ On the Fock space of metaanalytic functions ⋮ A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers ⋮ Some results on wavelet scalograms

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