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Weighted Radon Transforms of Three-Dimensional SymmetricTensor Fields of Rank Two Full article

Journal Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126
Output data Year: 2026, Volume: 36, Number: 1, Pages: 79-92 Pages count : 13 DOI: 10.1134/s1055134426010086
Tags tensor tomography, decomposition o fa tensor field, generalized Radon transform, weighted Radon transform, inversion formula
Authors Svetov I.E. 1,2 , Polyakova A.P. 1,2
Affiliations
1 Novosibirsk State University, Novosibirsk, 630090, Russia
2 Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

Funding (1)

1 Russian Science Foundation 24-21-00200

Abstract: We study properties of weighted Radon transforms of symmetric 2-tensor fields in R3. We establish connections between weighted Radon transforms of 2-tensor fields and the Radon transform of their potentials. These connections describe the kernel and image of tomographic integral operators acting on tensor fields. We consider formulations of problems on reconstruction of symmetric 2-tensor fields from the values of the normal, longitudinal, and weighted Radon transforms and obtain inversion formulas.
Cite: Svetov I.E. , Polyakova A.P.
Weighted Radon Transforms of Three-Dimensional SymmetricTensor Fields of Rank Two
Siberian Advances in Mathematics. 2026. V.36. N1. P.79-92. DOI: 10.1134/s1055134426010086 Scopus OpenAlex
Original: Svetov I.E. , Polyakova A.P.
Весовые преобразования Радона трёхмерных симметричных тензорных полей ранга 2
Математические труды. 2025. Т.28. №4. С.132-157. DOI: 10.25205/1560-750x-2025-28-4-132-157 OpenAlex
Identifiers:
≡ Scopus: 2-s2.0-105041799981
≡ OpenAlex: W7164843295
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