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This article is cited in 1 scientific paper (total in 1 paper)
Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data
Z. G. Medzhidov Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
Abstract:
A symmetric tensor field in the Euclidian space of any dimension ${{\mathbb R}}^n$ can be reconstructed from its integrals along straight lines which form n-manifold. We obtained the new formulas reconstructing solenoidal part of the fields when a ray transform is known only on complex lines, intersecting a given curve, as well as a curve belonging to infinity. The new family of two-dimensional planes in ${{\mathbb R}}^n$ is introduced and the inversion formula is obtained for the case of differential forms of degree $2$ on the given integrals along the planes of this family.
Keywords:
symmetric tensor field, ray transform, reconstruction, complex of lines, solenoidal part, Radon transform of differential forms.
Received: 25.10.2013 Revised: 21.05.2014 Accepted: 22.05.2014
Citation:
Z. G. Medzhidov, “Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data”, Daghestan Electronic Mathematical Reports, 2014, no. 1, 56–70
Linking options:
https://www.mathnet.ru/eng/demr5 https://www.mathnet.ru/eng/demr/y2014/i1/p56
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Abstract page: | 147 | Full-text PDF : | 35 | References: | 27 |
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