Uniqueness for the inverse backscattering problem for angularly controlled potentials

TL;DR

This paper proves that smooth, compactly supported potentials in R^3 are uniquely determined by their backscattering data if their difference has controlled angular derivatives, including differences expressed as finite spherical harmonic combinations.

Contribution

It establishes a uniqueness result for inverse backscattering problems with angular control conditions, extending previous understanding of potential recovery.

Findings

Uniqueness of potential recovery from backscattering data under angular derivative constraints.

Identification of potentials differing by spherical harmonic combinations with the same data.

Theoretical proof of uniqueness for a class of 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.