The Meijer transformation of generalized functions - E. L. Koh; E. Y. Deeba; M. A. Ali (International Journal of Mathematics and Mathematical Sciences)
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.