Radon–Kipriyanov Transform of Finite Functions

Radon–Kipriyanov transform ( $$K_{\gamma}$$ ) generalizes the results associated with the application of the Radon transform. This transform was introduced in 1998 by I.A. Kipriyanov and L.N. Lyakhov In theoretical and applied researches it is necessary to introduce its dual transform $$K_{\gamma}^{\#}.$$ Theorems on the boundedness of the transform $$K_{\gamma}^{\#}$$ in the corresponding subspace of compactly supported functions are proved. A formula for representing the generalized convolution of $$K_{\gamma}^{\#}$$ -transform is obtained.