Geodesic
On the transformation dual to the Radon--Kipriyanov transformation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 70-77

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The Radon–Kipriyanov transformation $K_\gamma$ was introduced in 1998. In various theoretical and applied research, the dual transformation $K_\gamma^{\#}$ is required. We prove theorems on the boundedness of the dual transformation in the corresponding L. Schwarz subspace of test functions and the $K_\gamma^{\#}$-transformation of the convolution of a function $g$ with the $K_\gamma[f]$-transformation, provided that both functions $g$ and $f$ belong to the corresponding spaces of test functions.
Mots-clés : Radon transform
Keywords: Radon–Kipriyanov transform, generalized Poisson shift, generalized mixed type shift, generalized convolution 
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     title = {On the transformation dual to the {Radon--Kipriyanov} transformation},
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L. N. Lyakhov; V. A. Kalitvin; M. G. Lapshina. On the transformation dual to the Radon--Kipriyanov transformation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 70-77. http://geodesic.mathdoc.fr/item/INTO_2024_232_a5/