The term “convolution” is commonly used in analysis. Best known examples of convolutions are the convolution of the Fourier, Laplace, and Mellin transforms. Broadly speaking, a convolution is always conceived as a bilinear, commutative and associative operation in a linear space, i.e., it is a multiplication in a linear space, such that the space itself becomes a commutative ring. There is a great variety of papers, articles, and books, in which the problems connected with investigation and using the convolutions are studied. We refer to L. Berg (1976), I.H. Dimovski (1982), I.H. Dimovski and V.S. Kiryakova (1984), I.H. Dimovski and S.L. Kalla (1988), H.-J. Glaeske and A. Heγ (1986), (1987), (1988), M. Goldberg (1961), S.I. Grozdev (1980), V.A. Kakichev (1967), (1990), V.S. Kiryakova (1989), Yu. F. Luchko and S.B. Yakubovich (1991), (1991a), N.A. Meller (1960), J. Mikusinski and G. Ryll-Nardzewski (1952), (1953), Nguyen Thanh Hai and S.B. Yakubovich (1992), J. Rodrigues (1990), M. Saigo and S.B. Yakubovich (1991), S.B. Yakubovich (1987a), (1987b), (1990), (1991a), (1991b), (1992), S.B. Yakubovich and Yu. F. Luchko (1991a), (1991b), S.B. Yakubovich and Nguyen Thanh Hai (1991), S.B. Yakubovich et al. (1992).