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2021 Classical and microlocal analysis of the x-ray transform on Anosov manifolds
Sébastien Gouëzel, Thibault Lefeuvre
Anal. PDE 14(1): 301-322 (2021). DOI: 10.2140/apde.2021.14.301

Abstract

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. ( 2 ) 190:1 (2019), 321–344). 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 Livšic theorem for Anosov flows, especially on a new quantitative finite-time Livšic theorem.

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Sébastien Gouëzel. Thibault Lefeuvre. "Classical and microlocal analysis of the x-ray transform on Anosov manifolds." Anal. PDE 14 (1) 301 - 322, 2021. https://doi.org/10.2140/apde.2021.14.301

Information

Received: 17 May 2019; Revised: 9 August 2019; Accepted: 7 October 2019; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.2140/apde.2021.14.301

Subjects:
Primary: 37C27 , 37D40 , 53C21 , 53C22 , 53C24

Keywords: Anosov flow , Hyperbolic dynamical systems , microlocal analysis , x-ray transform

Rights: Copyright © 2021 Mathematical Sciences Publishers

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