The generalized Lambert transform on distributions of compact support

In this paper we study the generalized Lambert transform introduced by Goldberg (Duke Math. J. 25 (1958) 459–476) and defined by F(x) = ∞ 0 f (t) ∞ k=1 ake−kxt dt, x >0, on the space E ((0,∞)) of distributions of compact support. An inversion formula is obtained over this space.  2002 Elsevier Science (USA). All rights reserved.