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On Radon transforms on compact Lie groups

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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
Published in
Proceedings of the American Mathematical Society
Authors
Ilmavirta, Joonas
Date
2016
Discipline
MatematiikkaMathematics
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.

 
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 Society
ISSN Search the Publication Forum
0002-9939
Keywords
Ray transforms Lie groups Fourier analysis inversio-ongelmat

Original source
http://www.ams.org/journals/proc/2016-144-02/S0002-9939-2015-12732-3/

DOI
https://doi.org/10.1090/proc12732
URI

http://urn.fi/URN:NBN:fi:jyu-201512224123

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/25384677

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