Inverse scattering on the half-line revisited

Abstract

The inverse scattering problem on the half-line has been studied in the literature in detail. V. Marchenko presented the solution to this problem. In this paper, the invertibility of the steps of the inver-sion procedure is discussed and a new set of necessary and sufficient conditions on the scattering data is given for the scattering data to be generated by a potential q ∈ L1,1. Our proof is new and in con-trast with Marchenko’s proof does not use equations on the negative half-line.