A class of index integral transforms. (English) Zbl 0623.44004
Rev. Tec. Fac. Ing., Univ. Zulia 10, No. 1, Ed. Espec., 105-118 (1987).
An integral transform with Meijer’s G-function in the kernel is investigated, which generalizes the transformation of J. Wimp [Proc. Edinb. Math. Soc., II. Ser. 14, 33-40 (1964; Zbl 0127.057)]. Spaces of originals are as well a space of functions which can be represented in the form of an inverse Mellin transform as the space \(L_ 2(0,\infty)\). In both cases conditions for the existence of the transform are given and an inversion formula is derived. The transform is a unitary transform of \(L_ 2(0,\infty)\). Finally some special cases are discussed.
Reviewer: H.-J.Glaeske
MSC:
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 33C60 | Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) |
