Wave operators on Sobolev spaces

Wave operators on Sobolev spaces

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...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2020-04, Vol.148 (4), p.1645-1652
1. Verfasser: Mizutani, Haruya
Format: Artikel
Sprache:eng
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Beschreibung
Zusammenfassung: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14838