Search results for "slab geometry"

showing 2 items of 2 documents

Tensor tomography in periodic slabs

2018

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.

Geodesicx-ray examinationslab geometrytomography01 natural sciencesinversio-ongelmatTensor fieldsymbols.namesaketomografiaMöbius stripTensor0101 mathematicsMathematical physicsMathematicsinverse problems010102 general mathematicsta111röntgentutkimusSymmetry (physics)Injective functionManifold010101 applied mathematicsKernel (algebra)symbolstensor tomographyX-ray tomographyAnalysisJournal of Functional Analysis
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Tensor tomography in periodic slabs

2017

The X-ray transform on the periodic slab $[0,1]\times\mathbb T^n$, $n\geq0$, 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 $m\geq0$. The characterization extends to more general manifolds, twisted slabs, including the M\"obius strip as the simplest example.

Mathematics - Differential GeometryMathematics - Functional Analysis44A12 53A45röntgenkuvausDifferential Geometry (math.DG)tomografiaFOS: Mathematicsröntgentutkimustensor tomographyslab geometryX-ray tomographyinversio-ongelmatFunctional Analysis (math.FA)
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