On Radon transforms on compact Lie groups
Abstract
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
.
Main Author
Format
Articles
Research article
Published
2016
Series
Subjects
Publication in research information system
Publisher
American Mathematical Society
Original source
http://www.ams.org/journals/proc/2016-144-02/S0002-9939-2015-12732-3/
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201512224123Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0002-9939
DOI
https://doi.org/10.1090/proc12732
Language
English
Published in
Proceedings of the American Mathematical Society
Citation
- Ilmavirta, J. (2016). On Radon transforms on compact Lie groups. Proceedings of the American Mathematical Society, 144(2), 681-691. https://doi.org/10.1090/proc12732
License
Copyright© 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.