6533b825fe1ef96bd1281f64

RESEARCH PRODUCT

Tensor tomography in periodic slabs

Gunther UhlmannGunther UhlmannJoonas Ilmavirta

subject

Geodesicx-ray examinationslab geometrytomography01 natural sciencesinversio-ongelmatTensor fieldsymbols.namesaketomografiaMöbius stripTensor0101 mathematicsMathematical physicsMathematicsinverse problems010102 general mathematicsta111röntgentutkimusSymmetry (physics)Injective functionManifold010101 applied mathematicsKernel (algebra)symbolstensor tomographyX-ray tomographyAnalysis

description

Abstract The X-ray transform on the periodic slab [ 0 , 1 ] × T n , n ≥ 0 , has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless n = 0 . We characterize the kernel of the geodesic X-ray transform for L 2 -regular m -tensors for any m ≥ 0 . The characterization extends to more general manifolds, twisted slabs, including the Mobius strip as the simplest example.

yearjournalcountryeditionlanguage
2018-07-01Journal of Functional Analysis
10.1016/j.jfa.2018.04.004https://doi.org/10.1016/j.jfa.2018.04.004