On Radon transforms on compact Lie groups
Finna-arvio
On Radon transforms on compact Lie groups
www.ams.org/journals...015-12732-3/
(Jyväskylän yliopisto - JYX)
ilmavirtaonradontransforms.pdf
(Jyväskylän yliopisto - JYX)
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 .
Tallennettuna:
Kieli |
englanti |
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Sarja | Proceedings of the American Mathematical Society, 2 |
Aiheet | |
ISSN |
0002-9939 |