Stability Estimates for the X-Ray Transform on Simple Asymptotically Hyperbolic Manifolds

TL;DR

This paper establishes stability estimates for the geodesic X-ray transform on functions within simple asymptotically hyperbolic manifolds by constructing a parametrix in the 0-pseudodifferential calculus.

Contribution

It introduces a novel parametrix construction for the normal operator of the X-ray transform in this geometric setting.

Findings

Proves a stability estimate for the X-ray transform.

Constructs a parametrix in the 0-pseudodifferential calculus.

Advances understanding of inverse problems on hyperbolic manifolds.

Abstract

We study the normal operator to the geodesic X-ray transform on functions in the setting of simple asymptotically hyperbolic manifolds. We construct a parametrix for the normal operator in the 0-pseudodifferential calculus and use it show a stability estimate.