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Stability estimates for the X-ray transform on simple asymptotically hyperbolic manifolds

Nikolas Eptaminitakis
Vol. 4 (2022), No. 3, 487–516
DOI: 10.2140/paa.2022.4.487
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 to show a stability estimate.

Keywords
asymptotically hyperbolic manifolds, X-ray transform, normal operator, stability, 0-calculus
Mathematical Subject Classification
Primary: 58J40
Secondary: 35R30
Milestones
Received: 1 June 2021
Revised: 29 April 2022
Accepted: 15 June 2022
Published: 4 December 2022
Authors
Nikolas Eptaminitakis
Institut für Differentialgeometrie
Leibniz Universität Hannover
Welfengarten 1
30167 Hannover
Germany