On inverse scattering for the multidimensional relativistic Newton equation at high energies

where V ∈ C(R,R), |∂ xV (x)| ≤ β|j|(1 + |x|)−(α+|j|) for |j| ≤ 2 and some α > 1. We give estimates and asymptotics for scattering solutions and scattering data for the equation (∗) for the case of small angle scattering. We show that at high energies the velocity valued component of the scattering operator uniquely determines the X-ray transform PF. Applying results on inversion of the X-ray transform P we obtain that for d ≥ 2 the velocity valued component of the scattering operator at high energies uniquely determines F . In addition we show that our high energy asymptotics found for the configuration valued component of the scattering operator doesn’t determine uniquely F . The results of the present work were obtained in the process of generalizing some results of Novikov [No] to the relativistic case.