Some problems in inverse scattering theory. (English) Zbl 0641.35053

Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1987, Exp. No. 3, 3 p. (1987).
We shall consider the Schrödinger operator \(H_ v=-\Delta +v(x)\) in \({\mathbb{R}}^ n\), where \(n=3,5,... \). We assume that \(v\in \nu\), i.e. \[ (1)\quad \int (1+| x|)^{| \alpha | -(n-2)}| v^{(\alpha)}(x)| dx<\infty \] for any \(\alpha\).
Some of the main problems we consider are the following:
(a) Analysis of bound states and poles of the scattering matrix.
(b) Backward scattering.
(c) The characterization problem for scattering matrices.
This talk will be a continuation of the author’s lecture at École Polytechnique [Semin., Equations Deriv. Partielles 1986-1987, 6 p. (1987)], and we shall mainly give some comments to (a).


35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
35R30 Inverse problems for PDEs
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