Classical and microlocal analysis of the x-ray transform on Anosov manifolds

International audienceWe complete the microlocal study of the geodesic X-ray transform on Riemannian manifolds with Anosov geodesic flow initiated by Guillarmou in [Gui17] and pursued by Guillarmou and the second author in [GL18]. We prove new stability estimates and clarify some properties of the operator Π m-the generalized X-ray transform. These estimates rely on a refined version of the Livsic theorem for Anosov flows, especially on a new quantitative finite time Livsic theorem