\Ve consider the direct and inverse scattering for the n-dimensional Schrodinger equation, n 2: 2, with a potential having no spherical symmetry. Sufficient conditions are given for the existence of a Wiener-Hopf factorization of the corresponding scattering operator. This factorization leads to the solution of a related Riemann-Hilbert problem, which plays a key role in inverse scattering.

1 Introduction In this lecture the author reviews his results on multidimensional inverse scattering. References to the works of other authors can be found in [20]. Five topics are briefly discussed:-1) property C with constraints and new type of the uniqueness theorems for inverse scattering,-2) inversion of noisy discrete fixed-energy 3D scattering data and error estimates,-3) variational pri...

The author studies the inverse scattering problem for a boundary value problem of a generalized one dimensional Schrödinger type with a discontinuous coefficient and eigenparameter dependent boundary condition. The solutions of the considered eigenvalue equation is presented and its scattering function that satisfies some properties is induced. The discrete spectrum is studied and the resolvent...

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When solving the inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential, one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko–Faddeev theorem [8] (in the continuous case, for the discrete case see [4, 6]), guarantees the uniqueness of the solution of the inve...

Abstract We consider phaseless inverse scattering for the multidimensional Schrödinger equation with unknown potential v using method of known background scatterers. In particular, in dimension d ⩾ 2, we show that | f 1 2 at high energies uniquely determines via explicit formulas, where is amplitude + w , an a priori nonzero scatterer, under condition supp and are sufficiently disjoint. If this...

Solving inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko– Faddeev theorem (in the continuous case) [6] and the Guseinov theorem (in the discrete case) [4], guarantees the uniqueness of solution of the...