6533b857fe1ef96bd12b3d1a

RESEARCH PRODUCT

On Radon Transforms on Tori

Joonas Ilmavirta

subject

Mathematics - Differential GeometryAstrophysics::High Energy Astrophysical PhenomenaGeneral Mathematicschemistry.chemical_elementRadoninversio-ongelmatTensor fieldray transformsMathematics - Analysis of PDEs46F12 44A12 53A45Dimension (vector space)FOS: MathematicsMathematicsgeometric opticsSolenoidal vector fieldRadon transformApplied MathematicsMathematical analysisOrder (ring theory)TorusFourier analysisDistribution (mathematics)Differential Geometry (math.DG)chemistryAnalysisAnalysis of PDEs (math.AP)

description

We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvi\`ere. We also show solenoidal injectivity of the X-ray transform on the $n$-torus for tensor fields of any order, allowing the tensors to have distribution valued coefficients. These imply new injectivity results for the periodic broken ray transform on cubes of any dimension.

yearjournalcountryeditionlanguage
2014-02-25
http://urn.fi/URN:NBN:fi:jyu-201510203418