The stability of inverse scattering with fixed energy

We consider a three-dimensional inverse scattering problem with fixed energy and with a spherically symmetrical, compactly supported potential. The resulting one-dimensional radial Schrrodinger operator defines the sequence of phase shifts. We give some estimates of the potential perturbation by the perturbation of the phase shifts. More precisely, an exact estimate is given for an integral norm of the potential perturbation by the forward differences of the normalized perturbation of phase shifts. Another upper bound is provided if only the first few phase shifts are available with some error.