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This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schrodinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in regularity in the local smoothing estimate. As an application, we apply well-known techniques to obtain well-posedness results for the semi-linear Schrodinger equation.

Cutoff resolvent estimates and the semilinear Schrödinger equation