English

Wave operators on Sobolev spaces

Analysis of PDEs 2019-09-05 v2

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 Schr\"odinger operators to which our abstract result applies. An application to scattering theory for the nonlinear Schr\"odinger equation with a potential is also given.

Keywords

Cite

@article{arxiv.1903.01719,
  title  = {Wave operators on Sobolev spaces},
  author = {Haruya Mizutani},
  journal= {arXiv preprint arXiv:1903.01719},
  year   = {2019}
}

Comments

6 pages; revised version; to appear in Proceedings of the AMS

R2 v1 2026-06-23T07:58:27.832Z