Recovery of singularities of a multidimensional scattering potential. (English) Zbl 0908.35092
Summary: We prove that in multidimensional potential scattering the leading order singularities of the unknown potential are obtained exactly from the scattering amplitude by the linearized inversion method. The proof is based on the appropriate mapping properties of the fundamental solution in weighted \(L^p\)-spaces and on a homogeneity argument concerning the bilinear term.