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Paper detail

X-ray tomography of one-forms with partial data

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.

preprint2021arXivOpen access
Joonas IlmavirtaKeijo Mönkkönen
math.FAmath.DG
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Joonas IlmavirtaKeijo Mönkkönen

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