Recovery of compactly supported spherically symmetric potentials from the phase shift of the S-wave

It is proved that the phase shift delta(0)(k) known for all k > 0, determines a real-valued locally integrable spherically symmetric potential q(x), \q(x)\ less than or equal to C exp(-c\x\(gamma)), gamma > 1, where gamma is a fixed number, c and C are positive constants. A procedure for finding the unknown potential from the above phase shift is proposed, an iterative process for finding the potential from the above data is described and its convergence is proved.