RECOVERY OF SINGULARITIES OF A MULTIDIMENSIONAL SCATTERING POTENTIAL

We prove that in multidimensional potential scattering the leading ord er singularities of the unknown potential are obtained exactly from th e scattering amplitude by the linearized inversion method. The proof i s based on the appropriate mapping properties of the fundamental solut ion in weighted L-p-spaces and on a homogeneity argument concerning th e bilinear term.