Abstract
We survey some basic problems of Schrödinger, Klein-Gordon and wave equations in the framework of general scattering theory. The following topics are treated under suitable decay and/or smallness conditions on the perturbation term: Growth estimates of generalized eigenfunctions, Resolvent estimates, Scattering direct and inverse problems, Smoothing properties and Strichartz estimates. Due to our formulation of the weighted energy method, some topics are naturally extended to time-dependent and/or non-selfadjoint perturbations.KeywordsResolvent estimatesScatteringSmoothing propertiesStrichartz estimatesMathematics Subject Classification81Q1081Uxx35R30
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