On Radon transforms on compact Lie groups

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 $S^1$.

13 pages

References in corpus (1)

• On the kernel of the maximal flat Radon transform on symmetric spaces of compact type

Cited by in corpus (4)

• Fourier analysis of periodic Radon transforms
• A geometric based preprocessing for weighted ray transforms with applications in SPECT
• A support theorem for the X-ray transform on manifolds with plane covers
• On Radon transforms on finite groups