Tensor tomography in periodic slabs
Ilmavirta, J., & Uhlmann, G. (2018). Tensor tomography in periodic slabs. Journal of Functional Analysis, 275(2), 288-299. https://doi.org/10.1016/j.jfa.2018.04.004
Published inJournal of Functional Analysis
© 2018 Elsevier Inc.
The X-ray transform on the periodic slab [0, 1]×Tn, 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 L2-regular m-tensors for any m ≥ 0. The characterization extends to more general manifolds, twisted slabs, including the Möbius strip as the simplest example.
ISSN Search the Publication Forum0022-1236
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Related funder(s)Academy of Finland
Funding program(s)Postdoctoral Researcher, AoF
Additional information about fundingJ.I. was supported by the Academy of Finland (decision 295853), and he is grateful for hospitality and support offered by the University of Washington during visits. G.U. was partly supported by NSF grant DMS-1265958, a Si-Yuan Professorship at IAS, HKUST, and a FiDiPro at University of Helsinki.
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