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 (Appl Comput Harmonic Anal 38(2):196–221, 2015)
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M. d. G. was supported by the grant P 23902 from the Austrian Science Fund (FWF). K. G. was supported in part by the project P26273-N25 of the Austrian Science Fund (FWF). J. L. R. gratefully acknowledges support from a Marie Curie fellowship, within the 7th European Community Framework program, under grant PIIF-GA-2012-327063.
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de Gosson, M.A., Gröchenig, K. & Romero, J.L. Stability of Gabor Frames Under Small Time Hamiltonian Evolutions. Lett Math Phys 106, 799–809 (2016). https://doi.org/10.1007/s11005-016-0846-6
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DOI: https://doi.org/10.1007/s11005-016-0846-6