Fixed energy inverse problem for exponentially decreasing potentials
偏微分方程分析
2007-05-23 v1
摘要
In this paper we show that in two-body scattering the scattering matrix at a fixed energy determines real-valued exponentially decreasing potentials. This result has been proved by Novikov previously, see also the work of Novikov and Khenkin using a d-bar-equation. We present a different method, which combines a density argument and real analyticity in part of the complex momentum. The latter has been noted by Novikov and Khenkin; here we give a short proof using contour deformations. In the addendum to the paper we also supply a reference to the work of Eskin and Ralston that did not appear in the published paper since we were unaware of the relevant aspects of their work.
引用
@article{arxiv.math/0307253,
title = {Fixed energy inverse problem for exponentially decreasing potentials},
author = {Gunther Uhlmann and Andras Vasy},
journal= {arXiv preprint arXiv:math/0307253},
year = {2007}
}
备注
Addendum added, on July 17, 2003, to the published version