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Wiener-Hopf factorization in multidimensional inverse Schrödinger scattering. (English) Zbl 0742.35044

Inverse scattering and applications, Proc. AMS-IMS-SIAM Conf., Amherst/MA (USA) 1990, Contemp. Math. 122, 1-11 (1991).
Summary: [For the entire collection see Zbl 0741.00079.]
We consider a Riemann-Hilbert problem arising in the study of the inverse scattering for the multidimensional Schrödinger equation with a potential having no spherical symmetry. It is shown that under certain conditions on the potential, the corresponding scattering operator admits a Wiener-Hopf factorization. The solution of the Riemann-Hilbert problem can be obtained using a similar factorization for the unitarily dilated scattering operator. We also study the connection between the Wiener-Hopf factorization and the Newton-Marchenko integral operator.

MSC:

35Q15 Riemann-Hilbert problems in context of PDEs
35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs
47A40 Scattering theory of linear operators

Citations:

Zbl 0741.00079
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