Symplectic and Hamiltonian Deformations of Gabor Frames
Functional Analysis
2013-05-07 v1 Mathematical Physics
math.MP
Quantum Physics
Abstract
We study symplectic deformations of Gabor frames using the covariance properties of the Heisenberg operators. This allows us to recover in a very simple way known results. We thereafter propose a general deformation scheme by Hamiltonian isotopies, which are paths of Hamiltonian flows. We define and study in detail a weak notion of Hamiltonian deformations, using ideas from semiclassical analysis due to Heller and Hagedorn. This method can be easily implemented using symplectic integrators.
Keywords
Cite
@article{arxiv.1305.1025,
title = {Symplectic and Hamiltonian Deformations of Gabor Frames},
author = {Maurice A. de Gosson},
journal= {arXiv preprint arXiv:1305.1025},
year = {2013}
}