Dual Radon—Kipriyanov transformation. Basic properties

L. N. Lyakhov^abc, V. A. Kalitvin^bd, M. G. Lapshina<sup>b

a</sup> Voronezh State University, Voronezh, Russia
^b Lipetsk State Pedagogical University named after P. P. Semenov-Tyan-Shanskiy, Lipetsk, Russia
^c Yelets State University named after I. A. Bunin, Yelets, Russia
^d Russian Presidential Academy of National Economy and Public Administration, Moscow, Russia

Abstract: The Radon–Kipriyanov transformation ($K_\gamma$) was introduced in 1998. In theoretical and applied studies, it is necessary to introduce its dual transformation, which is denoted by $K_\gamma^{\#}$ in the paper. Theorems on the boundedness of the $K_\gamma^{\#}$ transformation in the corresponding Schwartz subspace of the main functions are proved. A formula for representing the generalized convolution of $K_\gamma^{\#}$-transformations of functions belonging to the corresponding spaces of the main functions is obtained.

Keywords: Radon–Kipriyanov transformation, Fourier transformation, Fourier–Bessel transformation, generalized convolution.

UDC: 517.954

DOI: 10.22363/2413-3639-2024-70-4-643-653