X-ray Tomography of One-forms with Partial Data
Ilmavirta, J., & Mönkkönen, K. (2021). X-ray Tomography of One-forms with Partial Data. SIAM Journal on Mathematical Analysis, 53(3), 3002-3015. https://doi.org/10.1137/20M1344779
Published inSIAM Journal on Mathematical Analysis
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© 2021, Society for Industrial and Applied Mathematics
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.
PublisherSociety for Industrial & Applied Mathematics (SIAM)
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