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arXiv · 1511.00121

Stability of Gabor frames under small time Hamiltonian evolutions

Maurice A. de Gosson·Karlheinz Gröchenig·José Luis Romero
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Abstract

We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger 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 Sjöstrand 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.]

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Maurice A. de Gosson, Karlheinz Gröchenig, José Luis Romero. 2016-04-14. Stability of Gabor frames under small time Hamiltonian evolutions. https://doi.org/10.1007/s11005-016-0846-6

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