X-ray tomography of one-forms with partial data
Functional Analysis
2021-03-09 v2 Differential Geometry
Abstract
If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.
Keywords
Cite
@article{arxiv.2006.05790,
title = {X-ray tomography of one-forms with partial data},
author = {Joonas Ilmavirta and Keijo Mönkkönen},
journal= {arXiv preprint arXiv:2006.05790},
year = {2021}
}
Comments
15 pages, 1 figure. Final version