Regularity of Ghosts of the Geodesic X-Ray Transform

Michal Skokan
University of Washington

Date: July 29, 2004

We consider the X-ray transform of a symmetric tensor field on a simple compact Riemannian manifold with boundary. A tensor field that is orthogonal to the space of potential fields and for which the X-ray transform vanishes is called a nontrivial ghost. We prove that any nontrivial ghost is smooth up to the boundary and that the space of ghosts is finite dimensional. This is joint work with V. Sharafutdinov.