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Fixed energy inverse problem for exponentially decreasing potentials

Gunther Uhlmann·Andras Vasy
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Abstract

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.

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Gunther Uhlmann, Andras Vasy. 2003-07-17. Fixed energy inverse problem for exponentially decreasing potentials. https://arxiv.org/abs/math/0307253

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