Radon–Kipriyanov Transform of Finite Functions

Radon–Kipriyanov transform ( \(K_{\gamma}\) ) generalizes the resultsassociated with the application of the Radon transform. Thistransform was introduced in 1998 by I.A. Kipriyanov andL.N. Lyakhov In theoretical and applied researches it is necessaryto introduce its dual transform \(K_{\gamma}^{\#}.\) Theorems on theboundedness of the transform \(K_{\gamma}^{\#}\) in the correspondingsubspace of compactly supported functions are proved. A formulafor representing the generalized convolution of \(K_{\gamma}^{\#}\) -transform is obtained.