On the representation of the Radon—Kipriyanov transform by the Riesz potential

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

a</sup> Voronezh State University, Voronezh, Russia
^b Lipetsk State Pedagogical University named after P. P. Semenov-Tyan-Shansky, Lipetsk, Russia
^c Bunin Yelets State University, Yelets, Russia
^d Russian Presidential Academy of National Economy and Public Administration, Lipetsk Branch, Lipetsk, Russia
^e Financial University under the Government of the Russian Federation, Lipetsk Branch, Lipetsk, Russia

Abstract: In this paper, a representation of the Radon–Kipriyanov transform by the classical Riesz potential is obtained. Based on the application of the Radon–Kipriyanov transform to a singular partial differential operator, a formula for transformation of a linear singular partial differential operator into an ordinary (nonsingular) differential operator is obtained.

Keywords: Radon–Kipriyanov transform, Riesz potential, singular differential operator, partial derivatives.

UDC: 517.954

DOI: 10.22363/2413-3639-2025-71-2-267-274