Ray transform on Sobolev spaces of symmetric tensor fields, I: Higher order Reshetnyak formulas

Venky P. Krishnan, Vladimir A. Sharafutdinov

For an integer $r\ge 0$, we prove the $r$th order Reshetnyak formula for the ray transform of rank $m$ symmetric tensor fields on ${\mathbb{R}}^n$. Certain differential operators $A^{…