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On Radon transforms on compact Lie groups

Authors
  • Ilmavirta, Joonas
Type
Published Article
Publication Date
Jan 25, 2015
Submission Date
Oct 08, 2014
Identifiers
DOI: 10.1090/proc12732
Source
arXiv
License
Yellow
External links

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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