Double b-fibrations and desingularization of the X-ray transform on manifolds with strictly convex boundary

We study the mapping properties of the X-ray transform and its adjoint on spaces of conormal functions on Riemannian manifolds with strictly convex boundary. After desingularizing the double fibration, and expressing the X-ray transform and its adjoint using b-fibrations operations, we show that a näıve use of the pushforward Theorem leads to nonsharp index sets. We then refine these results using Mellin functions, showing that certain coefficients vanish; this recovers the sharpness of known results. A number of consequences for the mapping properties of the X-ray transform and its normal operator(s) follow.

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