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Classical and
microlocal analysis of the x-ray transform on Anosov
manifolds
Sébastien Gouëzel and Thibault Lefeuvre |
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Vol. 14 (2021), No. 1, 301–322
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Abstract |
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We complete the microlocal study of the geodesic x-ray transform on Riemannian manifolds with Anosov geodesic flow initiated by Guillarmou (J. Differential Geom. 105:2 (2017), 177–208) and pursued by Guillarmou and Lefeuvre in (Ann. of Math. 190:1 (2019), 321–344). We prove new stability estimates and clarify some properties of the operator — the generalized x-ray transform. These estimates rely on a refined version of the Livšic theorem for Anosov flows, especially on a new quantitative finite-time Livšic theorem. |
Keywords
Anosov flow, hyperbolic dynamical systems, x-ray transform,
microlocal analysis
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Mathematical Subject Classification 2010
Primary: 37C27, 37D40, 53C21, 53C22, 53C24
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Milestones
Received: 17 May 2019
Revised: 9 August 2019
Accepted: 7 October 2019
Published: 19 February 2021
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Authors |
| Sébastien Gouëzel | |
| Laboratoire Jean Leray, CNRS UMR
6629 Université de Nantes Nantes France |
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| Thibault Lefeuvre | |
| Laboratoire de Mathématiques
d’Orsay Université Paris-Sud, CNRS Université Paris-Saclay Orsay France |
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