Wave operators on Sobolev spaces

Mizutani, Haruya

doi:10.1090/proc/14838

Wave operators on Sobolev spaces
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by Haruya Mizutani PDF

Proc. Amer. Math. Soc. 148 (2020), 1645-1652 Request permission

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 for which our abstract result applies. An application to scattering theory for the nonlinear Schrödinger equation with a potential is also given.

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