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arXiv · 1310.5904

Wave packet analysis of Schrodinger equations in analytic function spaces

Elena Cordero·Fabio Nicola·Luigi Rodino
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Abstract

We consider a class of linear Schroedinger equations in R^d, with analytic symbols. We prove a global-in-time integral representation for the corresponding propagator as a generalized Gabor multiplier with a window analytic and decaying exponentially at infinity, which is transported by the Hamiltonian flow. We then provide three applications of the above result: the exponential sparsity in phase space of the corresponding propagator with respect to Gabor wave packets, a wave packet characterization of Fourier integral operators with analytic phases and symbols, and the propagation of analytic singularities.

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Elena Cordero, Fabio Nicola, Luigi Rodino. 2015-02-18. Wave packet analysis of Schrodinger equations in analytic function spaces. https://doi.org/10.1016/j.aim.2015.03.014

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