Scattering matrices with finite phase shift and the inverse scattering problem
The inverse scattering problem for the Schrodinger operator on the half-axis is studied. It is shown that this problem can be solved for the scattering matrices with arbitrary finite phase shift on the real axis if one admits potentials with long-range oscillating tails at infinity. The solution of the problem is constructed with the help of the Gelfand-Levitan-Marchenko procedure. The inverse pro