2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142255This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schrödinger 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 Schrödinger equation.8 pages, 1 figureAnalysis of PDEs35G25text