WIENER-HOPF FACTORIZATION IN THE INVERSE SCATTERING THEORY FOR THE n-D SCHRODINGER EQUATION

We study the n-dimensional Schrodinger equation, n 2 2, with a nonspherically symmetric potential in the class of Agmon's short range potentials without any positive energy bound states. We give sufficient conditions that guarantee the existence of a Wiener-Hopf factorization of the corresponding scattering operator. We show that the potential can be recovered from the scattering operator by solving a related Riemann-Hilbert problem utilizing the Wiener-Hopf factors of the scattering operator. We also study the properties of the scattering operator and show that it is a trace class perturbation of the identity when the potential is also integrable.