Article Dans Une Revue Russian Mathematical Surveys Année : 2021

Multipoint formulas for inverse scattering at high energies

Résumé

We consider inverse scattering for the multidimensional Schrödinger equation with smooth compactly supported potential v. We give explicit asymptotic formulas for the Fourier transform Fv(p) at fixed p in terms of the scattering amplitude f at n points at high energies. The precision of these formulas is proportional to n. To our knowledge these formulas are new for n≥ 2, whereas they reduce to the Born formula at high energies for n=1.

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hal-02983682 , version 1 (30-10-2020)

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Roman G Novikov. Multipoint formulas for inverse scattering at high energies. Russian Mathematical Surveys, 2021, 76 (4), pp.723-725. ⟨10.1070/RM9994⟩. ⟨hal-02983682⟩
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