Recovery of jumps and singularities in the multidimensional Schrodinger operator from limited data

Abstract

The inverse scattering problem for multidimensional Schrödinger operator is studied.More exactly we prove a new formula for the first nonlinear term to estimate more accuratelythis term. This estimate allows to concludethat all singularities and jumps of the unknown potential can be recovered from the Bornapproximation. Especially, we show for the potentials in $L^p$ for certain values of $p$ thatthe approximation agrees with the true potential up to the continuous function.% Text of abstract