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Inverse problems and microlocal analysis. (English) Zbl 0738.35053

Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1991, No.IX, 7 p. (1991).
In this lecture we discuss some recent problems in inverse scattering for the two-body Schrödinger operator \(H_ v=H_ 0+v\) in \(\mathbb{R}^ n\) where \(H_ 0=-\Delta\). The main part of the presentation will be devoted to the definition of exceptional points for \(H_ v\) and a study of the geometrical properties of the set \({\mathcal E}\) of such points. At the end of the lecture we explain briefly why the investigation of the set \({\mathcal E}\) is important in inverse scattering.

MSC:

35P25 Scattering theory for PDEs
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35R30 Inverse problems for PDEs
Full Text: Numdam EuDML