International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1987 / Article

Open Access

Volume 10 |Article ID 745171 | https://doi.org/10.1155/S0161171287000334

E. L. Koh, E. Y. Deeba, M. A. Ali, "The Meijer transformation of generalized functions", International Journal of Mathematics and Mathematical Sciences, vol. 10, Article ID 745171, 20 pages, 1987. https://doi.org/10.1155/S0161171287000334

The Meijer transformation of generalized functions

Received02 Jun 1986

Abstract

This paper extends the Meijer transformation, Mμ, given by (Mμf)(p)=2pΓ(1+μ)0f(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.

Copyright © 1987 Hindawi Publishing Corporation. 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.


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