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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 4, Pages 121–130 (Mi sjim810)  
This article is cited in 4 scientific papers (total in 4 papers)

Properties of the ray transforms of two-dimensional $2$-tensor fields given in the unit disk

I. E. Svetovab

a Novosibirsk State University, 2 Pirogov st., 630090 Novosibirsk
b Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
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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.
Received: 14.08.2013
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 1, Pages 106–114
DOI: https://doi.org/10.1134/S1990478914010128
Bibliographic databases:
Document Type: Article
UDC: 514.8+517.983
Language: Russian
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
Citation in format AMSBIB
\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}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал индустриальной математики
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