Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896628 | Journal of Functional Analysis | 2018 | 12 Pages |
Abstract
The X-ray transform on the periodic slab [0,1]ÃTn, nâ¥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 L2-regular m-tensors for any mâ¥0. The characterization extends to more general manifolds, twisted slabs, including the Möbius strip as the simplest example.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Joonas Ilmavirta, Gunther Uhlmann,