Pestov identities for generalized X-ray transforms

Pestov identities have proven useful in the study of X-ray tomography on Riemannian manifolds. After discussing previous triumphs of the method, we will extend it to new situations: broken ray tomography and X-ray tomography on pseudo-Riemannian manifolds. We will also discuss the limits of this method. This is partly joint work with Mikko Salo and Gabriel Paternain.