A representation of generalized Meijer-Laplace transform ablegeneralized functions

Abstract

In this paper, the spaces  H alpha, beta (I)  and its dual space H’ alpha,beta  (I)  are given. An extension of the generalized Meijer-Laplace transformation to a certain space of generalized functions (distributions) is given  and a structure formula for a class of generalized Meijer-Laplace transformable generalized functions  is obtained which shows that every element of the dual space of  H alpha, beta (I)  is the linear combination of  the finite order distributional derivative of continuous functions.