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Proceedings of the American Mathematical Society

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Wave operators on Sobolev spaces


Author: Haruya Mizutani
Journal: Proc. Amer. Math. Soc. 148 (2020), 1645-1652
MSC (2010): Primary 35P25; Secondary 35Q41, 35Q55
DOI: https://doi.org/10.1090/proc/14838
Published electronically: November 19, 2019
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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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Additional Information

Haruya Mizutani
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: haruya@math.sci.osaka-u.ac.jp

DOI: https://doi.org/10.1090/proc/14838
Received by editor(s): February 18, 2019
Received by editor(s) in revised form: August 20, 2019
Published electronically: November 19, 2019
Additional Notes: The author is is partially supported by JSPS KAKENHI Grant Numbers JP17K14218 and JP17H02854
Communicated by: Tanya Christiansen
Article copyright: © Copyright 2019 American Mathematical Society