Analytic smoothing effect for the Schrodinger equation with long-range perturbation

Martinez, Andre' ; Nakamura, Shu ; Sordoni, Vania (2005) Analytic smoothing effect for the Schrodinger equation with long-range perturbation. [Preprint]

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Abstract

We study microlocal analytic singularity of solutions to Schr\"odinger equation with analytic coefficients. Using microlocal weight estimate developped for estimating the phase space tunneling, we prove microlocal smoothing estimates that generalize results by L. Robbiano and C. Zuily. We suppose the Schr\"odinger operator is a long-range type perturbation of the Laplacian, and we employ positive commutator type estimates to prove the smoothing property.

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