Hamiltonian deformations of Gabor frames: first steps

DOI10.1016/j.acha.2014.03.010zbMath1306.81042arXiv1305.1025OpenAlexW2107179763WikidataQ39543812 ScholiaQ39543812MaRDI QIDQ2512832

Maurice A. De Gosson

Publication date: 30 January 2015

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

Full work available at URL: https://arxiv.org/abs/1305.1025

zbMATH Keywords

symplectic groupSchrödinger equationcoherent statessemiclassicalGabor framemetaplectic groupHamiltonian isotopy

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Coherent states (81R30) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (16)

Vector-valued (super) weaving frames ⋮ Stability of Gabor frames under small time Hamiltonian evolutions ⋮ Gabor frame sets of invariance: a Hamiltonian approach to Gabor frame deformations ⋮ Gabor frames of Gaussian beams for the Schrödinger equation ⋮ Semi-classical time-frequency analysis and applications ⋮ Discrete vector-valued nonuniform Gabor frames ⋮ Gabor analysis as contraction of wavelets analysis ⋮ Metaplectic Gabor frames and symplectic analysis of time-frequency spaces ⋮ On matrix-valued wave packet frames in \(L^2(\mathbb{R}^d, \mathbb{C}^{s\times r})\) ⋮ Minimal frame operator norms via minimal theta functions ⋮ Some curious results related to a conjecture of Strohmer and Beaver ⋮ Gaussian distributions and phase space Weyl-Heisenberg frames ⋮ On the parity under metapletic operators and an extension of a result of Lyubarskii and Nes ⋮ Multivariate Gabor frames for operators in matrix-valued signal spaces over locally compact abelian groups ⋮ A note on discrete wave packet frames in ℂN ⋮ Deformation of Gabor systems

Cites Work

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