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 in
Proceedings of the American Mathematical SocietyDate
2016Discipline
MatematiikkaCopyright
© 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
.
Publisher
American Mathematical SocietyISSN Search the Publication Forum
0002-9939Keywords