Geodesic
Support theorem for the Radon--Kipriyanov $K_\gamma$-transform
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 118-124

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The support theorem for the Radon transform was obtained by L. Helgason. The Radon transform of functions of groups of variables related by spherical symmetry is a special case of a more general transformation, namely, Radon–Kipriyanov transform $K_\gamma$. This transformation corresponds to a weight multi-index $\gamma=(\gamma_1,\ldots,\gamma_m)$ and coincides with Radon transform if all components of the multi-index $\gamma$ are natural numbers. In general, the $K_\gamma$-transformation can be interpreted as a transformation of functions of a fractional argument. In this paper, we prove a general support theorem. In a special case where $\gamma=0$, this theorem coincides with the Helgason theorem.
Mots-clés : Radon transform
Keywords: support theorem, Radon–Kipriyanov transform. 
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     title = {Support theorem for the {Radon--Kipriyanov} $K_\gamma$-transform},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     volume = {171},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a10/}
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L. N. Lyakhov; M. G. Lapshina; S. A. Roshchupkin. Support theorem for the Radon--Kipriyanov $K_\gamma$-transform. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 118-124. http://geodesic.mathdoc.fr/item/INTO_2019_171_a10/