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On Radon transforms on compact Lie groups


Author: Joonas Ilmavirta
Journal: Proc. Amer. Math. Soc. 144 (2016), 681-691
MSC (2010): Primary 46F12, 44A12, 22C05, 22E30
Published electronically: July 24, 2015
MathSciNet review: 3430844
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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$.


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Additional Information

Joonas Ilmavirta
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland
Email: joonas.ilmavirta@jyu.fi

DOI: https://doi.org/10.1090/proc12732
Keywords: Ray transforms, inverse problems, Lie groups, Fourier analysis
Received by editor(s): October 8, 2014
Received by editor(s) in revised form: January 21, 2015
Published electronically: July 24, 2015
Communicated by: Michael Hitrik
Article copyright: © Copyright 2015 American Mathematical Society