International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 267-286
doi:10.1155/S0161171287000334

The Meijer transformation of generalized functions

E. L. Koh,1 E. Y. Deeba,2 and M. A. Ali3

1Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, Canada
2Department of Applied Mathematical Sciences, University of Houston-Downtown, Houston 77002, Texas, USA
3#1598, Way 510, Muharraq 205, Bahrain

Received 2 June 1986

Copyright © 1987 E. L. Koh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper extends the Meijer transformation, Mμ, given by (Mμf)(p)=2pΓ(1+μ)∫0∞f(t)(pt)μ/2Kμ(2pt)dt, where f belongs to an appropriate function space, μ ϵ (−1,∞) and Kμ is the modified Bessel function of third kind of order μ, to certain generalized functions. A testing space is constructed so as to contain the Kernel, (pt)μ/2Kμ(2pt), of the transformation. Some properties of the kernel, function space and its dual are derived. The generalized Meijer transform, M¯μf, is now defined on the dual space. This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.