Gabor frames with Hermite functions

DOI10.1016/j.crma.2006.12.013zbMath1160.42013OpenAlexW2007696157MaRDI QIDQ868964

Karlheinz Gröchening, Yurij I. Lyubarskij

Publication date: 26 February 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2006.12.013

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Applications of hypergeometric functions (33C90)

Related Items (20)

Gabor (super)frames with Hermite functions ⋮ Gabor frames of Gaussian beams for the Schrödinger equation ⋮ Semi-classical time-frequency analysis and applications ⋮ Quasi-Banach modulation spaces and localization operators on locally compact abelian groups ⋮ Wavelet frames with Laguerre functions ⋮ Asymptotic expansion of polyanalytic Bergman kernels ⋮ On the representation and the uniform polynomial approximation of polyanalytic functions of Gevrey type on the unit disk ⋮ The mystery of Gabor frames ⋮ The canonical group of transformations of a Weyl-Heisenberg frame; applications to Gaussian and Hermitian frames ⋮ Banach Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group ⋮ On some Hermite series identities and their applications to Gabor analysis ⋮ Simultaneous estimates for vector-valued Gabor frames of Hermite functions ⋮ Discrete coherent states for higher Landau levels ⋮ Sampling and interpolation in Bargmann-Fock spaces of polyanalytic functions ⋮ On the structure of Gabor and super Gabor spaces ⋮ Paley‐Wiener estimates for the Heisenberg group ⋮ Weighted irregular Gabor tight frames and dual systems using windows in the Schwartz class ⋮ Designing Gabor windows using convex optimization ⋮ Uncertainty principle for multivector-valued functions ⋮ On the Fock space of metaanalytic functions

Cites Work

• 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
• On completeness of random exponentials in the Bargmann–Fock space
• The wavelet transform, time-frequency localization and signal analysis
• Harmonic Analysis in Phase Space. (AM-122)
• The Local Growth of Power Series: A Survey of the Wiman-Valiron Method
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