Email this article The Method of Approximate Inverse for Ray Transform Operators on Two-Dimensional Symmetric m-Tensor Fields
- Authors: Svetov I.E.1,2, Polyakova A.P.1,2, Maltseva S.V.1,2,3
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Lavrent’ev Institute of Hydrodynamics
- Issue: Vol 13, No 1 (2019)
- Pages: 157-167
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213153
- DOI: https://doi.org/10.1134/S1990478919010162
- ID: 213153
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Abstract
Two approaches are proposed for recovering a symmetric m-tensor field in a unit disk from the given values of ray transforms. The approaches are based on the method of approximate inverse. The first approach allows us to reconstruct all components of the tensor field, while the second recovers the potentials of the solenoidal part and m potential parts of the tensor field.
About the authors
I. E. Svetov
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: svetovie@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
A. P. Polyakova
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: apolyakova@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
S. V. Maltseva
Sobolev Institute of Mathematics; Novosibirsk State University; Lavrent’ev Institute of Hydrodynamics
Author for correspondence.
Email: maltsevasv@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090; pr. Akad. Lavrent’eva 15, Novosibirsk, 630090
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