The boundary regularity of the ghosts of the X-ray transform

Michal Skokan
UW

Date: March 5, 2004

We consider the X-ray transform of a symmetric tensor field of any rank on a simple compact Riemannian manifold with boundary. A symmetric tensor field in the kernel of the X-ray transform which is not potential is called a ghost. It is known that the ghosts of rank 2 are smooth at the boundary. We show the boundary regularity for the ghosts of any rank. Also, as a consequence we show that the dimension of the space of ghosts is finite. This is joint work with Vladimir Sharafutdinov.