Convolutions of generalized \(H\)-transforms (Q1842483)

The paper deals with a generalized transform of the Mellin type or \(H\)- transform. Such a generalized transform is defined via the generalized \(H\)-function of one variable. Conditions for the existence of convolutions of \(H\)-transforms are proved. The results are modifications of those by \textit{S. B. Yakubovich} and \textit{Nguyen Thanh Hai} [Izv. Vyssh. Uchebn. Zaved., Mat. 1991, No. 8(351), 72--79 (1991; Zbl 0745.44004)]. It is indicated that the results obtained can be extended to the multidimensional case. The two-dimensional case is considered and examples are given. In this connection see \textit{Vu Kim Tuan} [Dokl. Akad. Nauk Arm SSR 83, No. 1, 7--10 (1986; Zbl 0618.44005)], the first author [Sov. Math. (Iz. VUZ) 34, No. 2, 53--62 (1990; Zbl 0708.47022)] and \textit{S. B. Yakubovich} [Dokl. Akad. Nauk BSSR 34, No. 7, 588--591 (1990; Zbl 0715.44001)].