Journal of Lie Theory

no. 2
The Inversion of the X-ray Transform on a Compact Symmetric Space
Journal of Lie Theory, Volume 17 (2007) no. 2, pp. 307-315
The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M, proved in a previous paper of the author ["Totally geodesic spheres in compact symmetric spaces", Math. Ann. 165 (1966), 309--317].
DOI: 10.5802/jolt.448
Classification: 22E30, 43A85, 44A12, 53C65, 22E46, 53C35
Keywords: Compact symmetric spaces, Funk transform, Radon transform, X-ray transform 
@article{JOLT_2007_17_2_a4,
     author = {S. Helgason},
     title = {The {Inversion} of the {X-ray} {Transform} on a {Compact} {Symmetric} {Space}},
     journal = {Journal of Lie Theory},
     pages = {307--315},
     year = {2007},
     volume = {17},
     number = {2},
     doi = {10.5802/jolt.448},
     zbl = {1131.22006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.448/}
}
TY  - JOUR
AU  - S. Helgason
TI  - The Inversion of the X-ray Transform on a Compact Symmetric Space
JO  - Journal of Lie Theory
PY  - 2007
SP  - 307
EP  - 315
VL  - 17
IS  - 2
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.448/
DO  - 10.5802/jolt.448
ID  - JOLT_2007_17_2_a4
ER  - 
%0 Journal Article
%A S. Helgason
%T The Inversion of the X-ray Transform on a Compact Symmetric Space
%J Journal of Lie Theory
%D 2007
%P 307-315
%V 17
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.448/
%R 10.5802/jolt.448
%F JOLT_2007_17_2_a4
S. Helgason. The Inversion of the X-ray Transform on a Compact Symmetric Space. Journal of Lie Theory, Volume 17 (2007) no. 2, pp. 307-315. doi: 10.5802/jolt.448

Cited by Sources: