New rigorous asymptotic theorems for inverse scattering

Rigorous asymptotic theorems of both the integral and the local type, which were obtained earlier by the authors and which establish logarithmic and in some cases even power-law asymptotic correlations between the real and imaginary parts of the scattering amplitudes F/sub minus-or-plus/, are extended to the inverse amplitudes 1/F/sub minus-or-plus/. It has also been possible to establish a new type of power-law correlation between the real and imaginary parts of both the amplitudes and the inverse amplitudes. All of the results obtained here are quite suitable for experimental testing at high energies, where it can be assumed that the amplitudes have their asymptotic behavior