Abstract:
We study the longitudinal, transverse, and mixed ray transforms acting on two-dimensional symmetric 2-tensor fields. Namely, the kernels of the ray transforms are described; the connection between the ray transforms and the Radon transform is established; unconditional estimates of stability for each of the ray transforms are obtained; inversion formulas for a recovery of symmetric 2-tensor field components and for a recovery of the potential are obtained; projection theorems for the ray transforms are proved.
Keywords:
integral geometry, symmetric 2-tensor field, solenoidal field, potential field, longitudinal ray transform, transverse ray transform, mixed ray transform, estimate of stability, inversion formula, projection theorem.
Citation:
I. E. Svetov, “Properties of the ray transforms of two-dimensional 2-tensor fields given in the unit disk”, Sib. Zh. Ind. Mat., 16:4 (2013), 121–130; J. Appl. Industr. Math., 8:1 (2014), 106–114
\Bibitem{Sve13}
\by I.~E.~Svetov
\paper Properties of the ray transforms of two-dimensional $2$-tensor fields given in the unit disk
\jour Sib. Zh. Ind. Mat.
\yr 2013
\vol 16
\issue 4
\pages 121--130
\mathnet{http://mi.mathnet.ru/sjim810}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3234798}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 1
\pages 106--114
\crossref{https://doi.org/10.1134/S1990478914010128}
Linking options:
https://www.mathnet.ru/eng/sjim810
https://www.mathnet.ru/eng/sjim/v16/i4/p121
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