Vu Kim Tuan; Marichev, O. I.; Yakubovich, S. B. Composition structure of integral transformations. (English. Russian original) Zbl 0604.44003 Sov. Math., Dokl. 33, 166-170 (1986); translation from Dokl. Akad. Nauk SSSR 286, 786-790 (1986). The authors use Parseval’s identity for the Mellin transform introduce the G- and W-transforms, which include as special cases the most general classical convolution and index transforms, and the Wimp transform with Meyer G-function in the kernels. They define a new space of functions in which the composition structure of these transforms is explained. They establish theorems on conditions for the existence, invertibility, and composition decomposability of the G- and W-transforms in terms of the direct and inverse Laplace transforms with power multipliers in the space of functions introduced. Reviewer: S.P.Singh Cited in 9 Documents MSC: 44A15 Special integral transforms (Legendre, Hilbert, etc.) 44A10 Laplace transform Keywords:G-transform; Parseval’s identity; Mellin transform; W-transforms; convolution; index transforms; Wimp transform; Meyer G-function; existence; invertibility; composition decomposability; inverse Laplace transforms PDFBibTeX XMLCite \textit{Vu Kim Tuan} et al., Sov. Math., Dokl. 33, 166--170 (1986; Zbl 0604.44003); translation from Dokl. Akad. Nauk SSSR 286, 786--790 (1986)