Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in ${\mathbb{R}}^2$

Abstract

In this article, we study various aspects of the mixed ray transform of $(k+\ell )$-tensor fields that are symmetric in its first $k$ and last $\ell$ indices. As a first result, we derive an inversion algorithm to recover the solenoidal part of the unknown tensor field using the normal operator of the mixed ray transform. Next, we establish a set of unique continuation results. In addition to these, we discuss the range characterization of the mixed ray transform as the final result.