International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 267-286
The Meijer transformation of generalized functions
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.
This paper extends the Meijer transformation, , given by
where belongs to an appropriate function space, and is the modified Bessel function of third kind of order , to certain generalized functions. A testing space is constructed so as to contain the Kernel, , of the transformation. Some properties of the kernel, function space and its dual are derived. The generalized Meijer transform, , is now defined on the dual space. This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.