Wave packet analysis of Schrödinger equations in analytic function spaces |
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Authors: | Elena Cordero Fabio Nicola Luigi Rodino |
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Affiliation: | 1. Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy;2. Dipartimento di Scienze Matematiche, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy |
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Abstract: | We consider a class of linear Schrödinger equations in Rd, 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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Keywords: | 35Q41 35A20 35S05 35C15 42C15 |
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