Uniqueness for the inverse backscattering problem for angularly controlled potentials

Abstract

We consider the problem of recovering a smooth, compactly supported potential on R^3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled angular derivatives then the two potentials are identical. In particular, if two potentials differ by a finite linear combination of spherical harmonics with radial coefficinets and have the same backscattering data then the two potentials are identical.

This revision has a better introduction, a simpler proof of Theorem 1, and an appendix has been added which contains the derivation of the linearized problem and the relationship between the scattering data for a potential and its translate. The typing errors have been corrected, some references have been added and a different article format (with a larger font) has been used

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