2003/07/17 by Gunther Uhlmann, Andras Vasy · 1 citation
Mathematics · #math.AP #msc:81U40
published as Methods and Applications of Analysis 9:239-248 (2002) · Addendum added, on July 17, 2003, to the published version
arxiv created 2003/07/17 · arxiv updated 2009/12/01
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.