The Meijer transformation of generalized functions

E. L. Koh, E. Y. Deeba, M. A. Ali
1987 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, wherefbelongs to an appropriate function space,μ ϵ (−1,∞)andKμis the modified Bessel function of third kind of orderμ, 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
more » ... transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.
doi:10.1155/s0161171287000334 fatcat:hblkh3sidnag3p7oogdumv7equ