Wave operators on Sobolev spaces

Abstract

We provide a simple sufficient condition in an abstract framework to deduce the existence and completeness of wave operators (resp. modified wave operators) on Sobolev spaces from the existence and completeness of the usual wave operators (resp. modified wave operators). We then give some examples of Schrödinger operators to which our abstract result applies. An application to scattering theory for the nonlinear Schrödinger equation with a potential is also given.

arXiv comment6 pages; revised version; to appear in Proceedings of the AMS