Seminar

I will discuss a stability estimate for the geodesic X-ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and non-positive curvature.

The estimate is of the form $L^2\mapsto H^{1/2}_{T}$, where the $H^{1/2}_{T}$-space is defined using the natural parametrization of geodesics as initial boundary points and incoming directions (fan-beam geometry). Only tangential derivatives at the boundary are used. The proof is based on the observation that the Pestov identity with boundary term localizes in frequency. This estimate answers a question raised by Boman and Sharafutdinov.