Frames in Hermite-Bergman and special Hermite-Bergman spaces

DOI10.1007/s11868-016-0178-4zbMath1383.42032OpenAlexW2547332995MaRDI QIDQ1685338

Peng Zhang

Publication date: 13 December 2017

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11868-016-0178-4

zbMATH Keywords

Sobolev spacesBergman spacesframesGabor framesBessel sequencesHermite semigroupspecial Hermite functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General harmonic expansions, frames (42C15) Bergman spaces of functions in several complex variables (32A36) Bergman spaces and Fock spaces (30H20)

Related Items (1)

Sampling in the image of Sobolev space in \(L^2(\mathbb{R}, e^{u^2}du)\) under Schrödinger semigroup \(e^{it\Delta } \)

Cites Work

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• Frames in generalized Fock spaces
• Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform
• Irregular wavelet/Gabor frames
• The heat kernel transform for the Heisenberg group
• Frames in the bargmann space of entire functions
• Density theorems for sampling and interpolation in the Bargmann-Fock space I.
• Regular Sets of Sampling and Interpolation for Weighted Bergman Spaces
• Irregular Gabor frames and their stability
• Inversions of Hermite Semigroup

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