by Joonas Ilmavirta, Keijo Mönkkönen
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.
Reference:
X-ray tomography of one-forms with partial data (Joonas Ilmavirta, Keijo Mönkkönen), SIAM Journal on Mathematical Analysis, volume 53, pp. 3002–3015, 2021.
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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.
[arXiv]
Bibtex Entry:
@article{1f-partial-data-uc,
author = {Joonas Ilmavirta and Keijo M{\"o}nkk{\"o}nen},
title = {{X-ray tomography of one-forms with partial data}},
month = may,
journal = {SIAM Journal on Mathematical Analysis},
year = {2021},
volume = {53},
issue = {3},
pages = {3002--3015},
doi = {10.1137/20M1344779},
arxiv = {2006.05790},
url={http://users.jyu.fi/~jojapeil/pub/1f-partial-data-uc.pdf},
gsid = {1563462518400963356},
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.}
}