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RESEARCH PRODUCT
The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds
Joonas IlmavirtaKeijo Mönkkönensubject
Mathematics - Differential Geometryinverse problems44A12 53A99 86A22inversio-ongelmatFunctional Analysis (math.FA)Mathematics - Functional Analysisdifferentiaaligeometriageodesic ray transformDifferential Geometry (math.DG)FOS: MathematicsMathematics::Metric GeometryGeometry and TopologyMathematics::Differential GeometryMathematics::Symplectic Geometryintegral geometrydescription
We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to the invertibility of generalized Abel transforms and by Taylor expansions of geodesics we show that these Abel transforms are injective. Our result has applications in linearized boundary rigidity problem on Finsler manifolds and especially in linearized elastic travel time tomography.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2023-02-24 |