Geodesic
Inverse of the conic transformation of a function with a power weight
Daghestan Electronic Mathematical Reports, Tome 12 (2019), pp. 43-54

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We consider the Radon transformation defined on circular cones called the conical Radon transform. In the three-dimensio-nal space $R^{3}$, it maps the functions to its surface integrals over a circular cone, and in $R^{2}$ to its integrals over two rays with a common vertex. In this paper, we present new formulas for inversion of k-weighted conical and X-ray Radon transformations under complete and incomplete data in $R^{2}$ and $R^{3}$.
Keywords: conical transformation, k-weighted X-ray trans-formation, Radon transformation, inversion formula. 
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     author = {Z. G. Medzhidov},
     title = {Inverse of the conic transformation of a function with a power weight},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {43--54},
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     year = {2019},
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Z. G. Medzhidov. Inverse of the conic transformation of a function with a power weight. Daghestan Electronic Mathematical Reports, Tome 12 (2019), pp. 43-54. http://geodesic.mathdoc.fr/item/DEMR_2019_12_a3/