The X-ray transform on asymptotically conic spaces

Abstract

In this paper, partly based on Zachos' PhD thesis, we show that the geodesic X-ray transform is stably invertible near infinity on a class of asymptotically conic manifolds which includes perturbations of Euclidean space. In particular certain kinds of conjugate points are allowed. Further, under a global convex foliation condition, the transform is globally invertible. The key analytic tool, beyond the approach introduced by Uhlmann and Vasy, is the introduction of a new pseudodifferential operator algebra, which we name the 1-cusp algebra, and its semiclassical version.

39 pages, 5 figures

References in corpus (1)

• Resolvent near zero energy on Riemannian scattering (asymptotically conic) spaces

Cited by in corpus (1)

• The final state problem for the nonlinear Schrodinger equation in dimensions 1, 2 and 3