On Radon transforms on compact Lie groups
Ilmavirta, J. (2016). On Radon transforms on compact Lie groups. Proceedings of the American Mathematical Society, 144 (2), 681-691. doi:10.1090/proc12732
Published inProceedings of the American Mathematical Society
© 2015 American Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by AMS. Published in this repository with the kind permission of the publisher.
We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S 1 nor to S 3 . This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms from S 1 .
PublisherAmerican Mathematical Society