Stability of Gabor frames under small time Hamiltonian evolutions
Mathematical Physics
2016-11-29 v2 Classical Analysis and ODEs
math.MP
Abstract
We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schr\"odinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability of the frame property for small times and Hamiltonians consisting of a quadratic polynomial plus a potential in the Sj\"ostrand class with bounded second order derivatives. This answers a question raised in [de Gosson, M. Symplectic and Hamiltonian Deformations of Gabor Frames. Appl. Comput. Harmon. Anal. Vol. 38 No.2, (2015) p.196--221.]
Cite
@article{arxiv.1511.00121,
title = {Stability of Gabor frames under small time Hamiltonian evolutions},
author = {Maurice A. de Gosson and Karlheinz Gröchenig and José Luis Romero},
journal= {arXiv preprint arXiv:1511.00121},
year = {2016}
}
Comments
11 pages. Minor revision