Geodesic
The ray transform of symmetric tensor fields with incomplete projection data on a convex non-smooth domain
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1011-1023 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the ray transform $I_\Gamma$ that integrates symmetric rank $m$ tensor fields on $\mathbb{R}^n$ supported in a bounded convex domain $D \subset \mathbb{R}^n$ over lines. The integrals are known for the family $\Gamma$ of lines $l$ such that endpoints of the segment $l \cap D$ belong to a given part $\gamma = \partial D \cap \mathbb{R}^n_{+}$ of the boundary, for some half-space $R^n_{+}\subset \mathbb{R}^n$. In this work, we assume that the domain $D$ is convex with a non-smooth boundary. In this case, we prove that the kernel of the operator $I_\Gamma$ coincides with the space of $\gamma$-potential tensor fields, which is a generalization of the results obtained in [2].
Keywords: tomography with incomplete data, ray transform, tensor analysis. 
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N. A. Vaytsel. The ray transform of symmetric tensor fields with incomplete projection data on a convex non-smooth domain. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1011-1023. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a59/

[1] S. Helgason, The Radon Transform, 2nd ed., Birkhäuser, Boston, 1999 https://math.mit.edu/h̃elgason/Radonbook.pdf | Zbl

[2] V.A. Sharafutdinov, “The ray transform of symmetric tensor fields with incomplete projection data, I: the kernel of transform”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1219–1237 http://semr.math.nsc.ru/v18/n2/p1219-1237.pdf | DOI | Zbl

[3] V.A. Sharafutdinov, Integral geometry of tensor fields, VSP, Utrecht, 1994 http://old.math.nsc.ru/s̃harafutdinov/files/book.pdf | Zbl