Geodesic
Properties of the ray transforms of two-dimensional $2$-tensor fields given in the unit disk
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 121-130

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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, mixed ray transform, estimate of stability, projection theorem.
Mots-clés : transverse ray transform, inversion formula 
@article{SJIM_2013_16_4_a10,
     author = {I. E. Svetov},
     title = {Properties of the ray transforms of two-dimensional $2$-tensor fields given in the unit disk},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {121--130},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_4_a10/}
}
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I. E. Svetov. Properties of the ray transforms of two-dimensional $2$-tensor fields given in the unit disk. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 121-130. http://geodesic.mathdoc.fr/item/SJIM_2013_16_4_a10/