Decomposition of symmetric tensor fields in $\mathbb{R}^3$

I. E. Svetov; A. P. Polyakova

Geodesic

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Decomposition of symmetric tensor fields in $\mathbb{R}^3$

I. E. Svetov ; A. P. Polyakova

Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 1, pp. 161-178

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Résumé

In the article, we introduce generalizations of the curl operator acting on three-dimensional symmetric $m$-tensor fields and establish properties of them. For the spaces of three-dimensional tensor fields, new detailed decompositions are obtained. Each term in the decompositions is constructed using of one function. Decompositions of this kind play a special role, in particular, in the study of tomographic integral operators acting on symmetric $m$-tensor fields, $m\geqslant1$, and in the construction of algorithms for solving the emerging inverse problems.

Keywords: decomposition of symmetric tensor field, solenoidal field, potential field, potential, curl operator, computerized tomography, ray transform
Mots-clés : Radon transform. .

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     author = {I. E. Svetov and A. P. Polyakova},
     title = {Decomposition of symmetric tensor fields in $\mathbb{R}^3$},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {161--178},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_1_a14/}
}

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I. E. Svetov; A. P. Polyakova. Decomposition of symmetric tensor fields in $\mathbb{R}^3$. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 1, pp. 161-178. http://geodesic.mathdoc.fr/item/SJIM_2023_26_1_a14/