6533b82ffe1ef96bd129467c
RESEARCH PRODUCT
On Radon transforms on compact Lie groups
Joonas Ilmavirtasubject
Mathematics - Differential GeometryPure mathematicsGeodesicGeneral MathematicsGroup Theory (math.GR)inversio-ongelmatsymbols.namesake46F12 44A12 22C05 22E30FOS: MathematicsRepresentation Theory (math.RT)MathematicsRadon transformLie groupsinverse problemsApplied Mathematicsta111Lie groupTorusInverse problemInjective functionFourier analysisDifferential Geometry (math.DG)Fourier analysissymbolsRay transformsHomomorphismMathematics - Group TheoryMathematics - Representation Theorydescription
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 $S^1$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |