On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity

Abstract

We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.

This is a slightly edited version of the previous paper

References in corpus (1)

• Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

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• High-energy and smoothness asymptotic expansion of the scattering amplitude for the Dirac equation and applications
• Inverse scattering at fixed energy for radial magnetic Schr{ö}dinger operators with obstacle in dimension two