The Light Ray Transform on Lorentzian Manifolds

被引：0
|
作者：
Matti Lassas
Lauri Oksanen
Plamen Stefanov
Gunther Uhlmann
机构：
[1] University of Helsinki,Department of Mathematics and Statistics
[2] University College London,Department of Mathematics
[3] Purdue University,Department of Mathematics
[4] University of Washington,Department of Mathematics
[5] IAS,undefined
[6] HKUST,undefined
来源：
Communications in Mathematical Physics | 2020年 / 377卷
关键词：
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the weighted light ray transform L of integrating functions on a Lorentzian manifold over lightlike geodesics. We analyze L as a Fourier Integral Operator and show that if there are no conjugate points, one can recover the spacelike singularities of a function f from its the weighted light ray transform Lf by a suitable filtered back-projection.
引用
收藏
页码：1349 / 1379
页数：30
相关论文
共 50 条
  • [1] The Light Ray Transform on Lorentzian Manifolds
    Lassas, Matti
    Oksanen, Lauri
    Stefanov, Plamen
    Uhlmann, Gunther
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2020, 377 (02) : 1349 - 1379
  • [2] SUPPORT THEOREMS FOR THE LIGHT RAY TRANSFORM ON ANALYTIC LORENTZIAN MANIFOLDS
    Stefanov, Plamen
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (03) : 1259 - 1274
  • [3] The Light Ray Transform in Stationary and Static Lorentzian Geometries
    Ali Feizmohammadi
    Joonas Ilmavirta
    Lauri Oksanen
    The Journal of Geometric Analysis, 2021, 31 : 3656 - 3682
  • [4] The Light Ray Transform in Stationary and Static Lorentzian Geometries
    Feizmohammadi, Ali
    Ilmavirta, Joonas
    Oksanen, Lauri
    JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (04) : 3656 - 3682
  • [5] On a variational theory of light rays on Lorentzian manifolds
    Att Aca Naz Lincei Cl Sci Fis Mat Nat Rend Lincei Mat Appl, 3 (155):
  • [6] Ray transform on Riemannian manifolds
    Sharafutdinov, VA
    NEW ANALYTIC AND GEOMETRIC METHODS IN INVERSE PROBLEMS, 2004, : 187 - 259
  • [7] Reconstruction of Lorentzian Manifolds from Boundary Light Observation Sets
    Hintz, Peter
    Uhlmann, Gunther
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019, 2019 (22) : 6949 - 6987
  • [8] A Morse Theory for light rays on stably causal Lorentzian manifolds
    Giannoni, F
    Masiello, A
    Piccione, P
    ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE, 1998, 69 (04): : 359 - 412
  • [9] Lorentzian similarity manifolds
    Kamishima, Yoshinobu
    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2012, 10 (05): : 1771 - 1788
  • [10] An imbedding of Lorentzian manifolds
    Kim, Do-Hyung
    CLASSICAL AND QUANTUM GRAVITY, 2009, 26 (07)
12345