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Resolvent Estimates and Scattering Problems for Schrödinger, Klein-Gordon and Wave Equations

  • Kiyoshi MochizukiEmail author
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 44)

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.

Keywords

Resolvent estimates Scattering Smoothing properties Strichartz estimates 

Mathematics Subject Classification

81Q10 81Uxx 35R30 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Department of MathematicsChuo UniversityTokyoJapan

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