SOME THEOREMS ON A GENERALIZED LAPLACE TRANSFORM OF GENERALIZED FUNCTIONS

In this paper we extend the generalized Laplace transform \[F(s)=\frac{\Gamma(\beta+\eta+1)}{\Gamma(\alpha+\beta+\eta+1)}\int_0^\infty (st)^\beta\ _1F_1(\beta+\eta+1, \alpha+\beta+\eta+1; -st)f(t) dt\]where $f(t)\in L(0,\infty)$, $\beta\ge 0$, $\eta > 0$; to a class of generalized functions. We will extend the above transform to a class of generalized functions as a special case of the convolution  transform and prove an inversion formula for it.