X-RAY TRANSFORM ON DAMEK-RICCI SPACES

被引：6

作者：

Rouviere, Francois ^{[1
]}

机构：

[1] Univ Nice, Lab JA Dieudonne, F-06108 Nice 2, France

来源：

INVERSE PROBLEMS AND IMAGING | 2010年 / 4卷 / 04期

关键词：

Damek-Ricci space; hyperbolic space; X-ray transform; totally geodesic submanifold;

D O I：

10.3934/ipi.2010.4.713

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Damek-Ricci spaces, also called harmonic NA groups, make up a large class of harmonic Riemannian manifolds including all hyperbolic spaces. We prove here an inversion formula and a support theorem for the X-ray transform, i.e. integration along geodesics, on those spaces. Using suitably chosen totally geodesic submanifolds we reduce the problems to similar questions on low-dimensional hyperbolic spaces.

引用

页码：713 / 720

页数：8

共 50 条

[11] THE X-RAY TRANSFORM ON ASYMPTOTICALLY CONIC SPACES
Vasy, Andras
Zachos, Evangelie
PURE AND APPLIED ANALYSIS, 2024, 6 (03): : 693 - 730
[12] THE TENSORIAL X-RAY TRANSFORM ON ASYMPTOTICALLY CONIC SPACES
Jia, Qiuye
Vasy, Andras
INVERSE PROBLEMS AND IMAGING, 2024, 18 (04) : 908 - 942
[13] The X-ray transform for currents
David, L
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2003, 18 (01) : 113 - 117
[14] Domains with algebraic X-ray transform
Agranovsky, Mark
ANALYSIS AND MATHEMATICAL PHYSICS, 2022, 12 (02)
[15] Functions of constant geodesic x-ray transform
Ilmavirta, Joonas
Paternain, Gabriel P.
INVERSE PROBLEMS, 2019, 35 (06)
[16] ON THE INJECTIVITY OF THE X-RAY TRANSFORM FOR ANOSOV THERMOSTATS
Jane, Dan
Paternain, Gabriel P.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (02) : 471 - 487
[17] An efficient algorithm to compute the X-ray transform
Chen, Chong
Wang, Runqian
Bajaj, Chandrajit
Oktem, Ozan
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2022, 99 (07) : 1325 - 1343
[18] The inversion of the X-ray transform on a compact symmetric space
Helgason, Sigurdur
JOURNAL OF LIE THEORY, 2007, 17 (02) : 307 - 315
[19] ON RANGE CONDITION OF THE TENSOR X-RAY TRANSFORM IN Rn
Denisiuk, Aleksander
INVERSE PROBLEMS AND IMAGING, 2020, 14 (03) : 423 - 435
[20] Iterative inversion of the tensor momentum x-ray transform
Denisiuk, Aleksander
INVERSE PROBLEMS, 2023, 39 (10)

← 1 2 3 4 5 →