an:03975589
Zbl 0604.44003
Vu Kim Tuan; Marichev, O. I.; Yakubovich, S. B.
Composition structure of integral transformations
EN
Sov. Math., Dokl. 33, 166-170 (1986); translation from Dokl. Akad. Nauk SSSR 286, 786-790 (1986).
00180143
1986
j
44A15 44A10
G-transform; Parseval's identity; Mellin transform; W-transforms; convolution; index transforms; Wimp transform; Meyer G-function; existence; invertibility; composition decomposability; inverse Laplace transforms
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.
S.P.Singh