Geodesic
An analog of the Paley--Wiener theorem for the Radon $K_\gamma$-transform for integer $|\gamma|$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 104-109

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The study of the Radon transformation based on weighted plane waves was initiated by I. A. Kipriyanov. In this paper, we obtain necessary and sufficient conditions satisfied by the Radon $K_\gamma$-transform of smooth functions that decrease together with all their derivatives.
Keywords: Paley–Wiener theorem, Radon–Kipriyanov transform, inversion of the Radon transform, inversion of the Radon–Kipriyanov transform.
Mots-clés : Radon transform 
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     title = {An analog of the {Paley--Wiener} theorem for the {Radon} $K_\gamma$-transform for integer $|\gamma|$},
     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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L. N. Lyakhov; M. G. Lapshina. An analog of the Paley--Wiener theorem for the Radon $K_\gamma$-transform for integer $|\gamma|$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 104-109. http://geodesic.mathdoc.fr/item/INTO_2021_193_a10/