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Article Dans Une Revue Analysis & PDE Année : 2021

Classical and microlocal analysis of the x-ray transform on Anosov manifolds

Thibault Lefeuvre
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Résumé

We complete the microlocal study of the geodesic X-ray transform on Riemannian manifolds with Anosov geodesic flow initiated by Guillarmou in [Gui17] and pursued by Guillarmou and the second author in [GL18]. We prove new stability estimates and clarify some properties of the operator Π m-the generalized X-ray transform. These estimates rely on a refined version of the Livsic theorem for Anosov flows, especially on a new quantitative finite time Livsic theorem.
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Dates et versions

hal-03400842 , version 1 (25-10-2021)

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Sébastien Gouëzel, Thibault Lefeuvre. Classical and microlocal analysis of the x-ray transform on Anosov manifolds. Analysis & PDE, 2021, 14 (1), pp.301-322. ⟨10.2140/apde.2021.14.301⟩. ⟨hal-03400842⟩
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