CLASSICAL AND MICROLOCAL ANALYSIS OF THE X-RAY TRANSFORM ON ANOSOV MANIFOLDS

被引：6

作者：

Gouezel, Sebastien ^{[1
]}

Lefeuvre, Thibault ^{[2
]}

机构：

[1] Univ Nantes, Lab Jean Leray, CNRS UMR 6629, Nantes, France

[2] Univ Paris Saclay, CNRS, Univ Paris Sud, Lab Math Orsay, Orsay, France

来源：

ANALYSIS & PDE | 2021年 / 14卷 / 01期

基金：

欧洲研究理事会;

关键词：

Anosov flow; hyperbolic dynamical systems; x-ray transform; microlocal analysis; INVARIANT DISTRIBUTIONS; SPECTRAL RIGIDITY; REGULARITY;

D O I：

10.2140/apde.2021.14.301

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Pi(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.

引用

页码：301 / 322

页数：22

共 50 条

[31] X-ray transform and 3D Radon transform for ellipsoids and tetrahedra
Zhu, Jiehua
Lee, Seung Wook
Ye, Yangbo
Zhao, Shiying
Wang, Ge
JOURNAL OF X-RAY SCIENCE AND TECHNOLOGY, 2004, 12 (04) : 215 - 229
[32] Microlocal analysis of the Doppler transform on R3
Ramaseshan, K
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2004, 10 (01) : 73 - 82
[33] Single Pixel X-ray Transform and Related Inverse Problems
Lai, Ru-Yu
Uhlmann, Gunther
Zhai, Jian
Zhou, Hanming
SIAM JOURNAL ON IMAGING SCIENCES, 2022, 15 (04) : 1894 - 1909
[34] SINGULARITIES OF THE X-RAY TRANSFORM AND LIMITED DATA TOMOGRAPHY IN R(2) AND R(3)
QUINTO, ET
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (05) : 1215 - 1225
[35] Fast parallel algorithms for the x-ray transform and its adjoint
Gao, Hao
MEDICAL PHYSICS, 2012, 39 (11) : 7110 - 7120
[36] CARLEMAN ESTIMATES FOR GEODESIC X-RAY TRANSFORMS
Paternain, Gabriel P.
Salo, Mikko
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2023, 56 (05): : 1339 - 1379
[37] Microlocal analysis for spherical Radon transform: two nonstandard problems
Nguyen, Linh, V
Pham, Tuan A.
INVERSE PROBLEMS, 2019, 35 (07)
[38] Stability of the Non-abelian X-ray Transform in Dimension ≥ 3
Bohr, Jan
JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (11) : 11226 - 11269
[39] Admissible Complexes for the Projective X-ray Transform over a Finite Field
Feldman, David, V
Grinberg, Eric L.
DISCRETE & COMPUTATIONAL GEOMETRY, 2020, 64 (01) : 28 - 36
[40] ON THE RANGE OF THE X-RAY TRANSFORM OF SYMMETRIC TENSORS COMPACTLY SUPPORTED IN THE PLANE
Sadiq, Kamran
Tamasan, Alexandru
INVERSE PROBLEMS AND IMAGING, 2022, : 660 - 685

← 1 2 3 4 5 →