APPLICATIONS OF GENERALIZED CONVOLUTIONS ASSOCIATED WITH THE FOURIER AND HARTLEY TRANSFORMS

摘要

In this paper we present new generalized convolutions with weight-function associated with the Fourier and Hartley transforms, and consider applications. Namely, using the generalized convolutions, we construct normed rings on the space L~1 (R~d), provide the sufficient and necessary condition for the solvability of a class of integral equations of convolution type, and receive the explicit solutions of those equations.