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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Radon transforms on compact Lie groups
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by Joonas Ilmavirta PDF
Proc. Amer. Math. Soc. 144 (2016), 681-691 Request permission

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
  • MR Author ID: 1014879
  • Email: joonas.ilmavirta@jyu.fi
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 681-691
  • MSC (2010): Primary 46F12, 44A12, 22C05, 22E30
  • DOI: https://doi.org/10.1090/proc12732
  • MathSciNet review: 3430844