Ray transform on Sobolev spaces of symmetric tensor fields, II: Range characterization

The ray transform $I$ integrates symmetric $m$-tensor field in $\mathbb{R}^n$over lines. This transform in Sobolev spaces was studied in our earlier workwhere higher order Reshetnyak formulas (isometry relations) were established.The main focus of the current work is the range characterization. In dimensions$n\geq 3$, the range characterization of the ray transform in Schwartz spacesis well-known; the main ingredient of the characterization is a system oflinear differential equations of order $2(m+1)$ which are called Johnequations. Using the higher order Reshetnyak formulas, the range of the raytransform on Sobolev spaces is characterized in dimensions $n\geq 3$ in thispaper.