The Meijer Transformation of Generalized Functions
نویسنده
چکیده
This paper extends the Meijer transformation, M, given by I /2K 2p f(t) (pt) (2 p)dt, (Mf) (p) (i+) 0 where f belongs to an appropriate function space, e (-1,) and K is the modified Bessel function of third kind of order , to certain generalized functions. A testing space is constructed so as to contain the (pt)/2K(2p), of the transformation. Some properties of the kernel, function space and its dual are derived. The generalized Meijer transform, f, is now defined on the dual space. This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.
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