Properties of the ray transforms of two-dimensional 2-tensor fields defined in the unit disk

Abstract

We study the longitudinal, transverse, and mixed ray transforms acting on two-dimensional symmetric 2-tensor fields. Namely, the kernels of the ray transforms are described; the connection between the ray transforms and the Radon transform is established; some unconditional estimates of stability for each of the ray transforms are obtained; inversion reconstruction formulas for the components of the symmetric 2-tensor and for the recovery of the potential are deduced; and the projection theorems for the ray transforms are proved as well.