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Intertwining methods in the problem of inverse scattering. (English) Zbl 0618.35029
Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1986, Conf. No. 5, 8 p. (1986).
Let $$H_ v$$ be the Schrödinger operator with a short range potential v(x), A be the intertwining operator: $$H_ vA=AH_ 0$$. By using a fundamental solution of the ultrahyperbolic operator $$\Delta_ x- \Delta_ y$$, the author obtains explicit expressions for the intertwining operator A, for wave operators $$W_{\pm}=\lim_{t\to \pm \infty} e^{itH}ve^{-itH}0$$, and a formula for the scattering operator $$S=W^*_+W_-.$$
These results are applied to the inverse scattering problems.
Reviewer: S.Tajima

##### MSC:
 35J10 Schrödinger operator, Schrödinger equation 35P25 Scattering theory for PDEs 35R30 Inverse problems for PDEs 47A40 Scattering theory of linear operators
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