On Even and Odd Radon–Kipriyanov Transformations.

The previously introduced Radon–Kipriyanov transformation is adapted for the study of singular differential Bessel operators of even order : , . In this paper, the odd Radon–Kipriyanov transform and full Radon–Kipriyanov transform are introduced to study more general equations containing odd B-derivatives , (in particular, gradients of functions). Formulas for the complete Radon–Kipriyanov transformation of the corresponding linear singular differential operators are obtained. Based on the Bessel transformations (direct and inverse) introduced by B.M. Levitan, and "odd" Bessel transformations (direct and inverse) introduced by I.A. Kipriyanov and V.V. Katrakhov, a connection is obtained between the complete Radon–Kipriyanov transform with the Fourier transform and the mixed Fourier–Levitan–Kipriyanov–Katrakhov transform. The basic elementary properties of the complete Radon–Kipriyanov transformation are given. [ABSTRACT FROM AUTHOR]