Leonid Pestov
Institute of Computational Mathematics and Mathematical Geophysics,
Novisibirsk, Russia
Date: November 2, 2004
We describe a relation between the scattering relation, the Hilbert transform in frequency space and the geodesic ray transform for simple, two dimensional compact Riemannian manifolds with boundary. We use this relation to give a characterization of the range of the geodesic X ray transform acting on scalar functions and vector fields in terms of the scattering relation which involves only measurements at the boundary. We also give inversion formulas for the geodesic X-ray transform acting on scalar functions and vector fields.