On a generalization of Laplace transform due to E. Krätzel. (English) Zbl 0844.44002

Summary: We study an integral transform introduced by E. Krätzel and denoted by \(L_{\nu,n}\) that generalizes the well-known Laplace and Meijer transformations. We establish two new real inversion formulas for \(L_{\nu,n}\). In the first formula we employ differential operators of infinite order and in the second one we use a differential operator which generalizes the Post-Widder operator. We also prove Abelian and Tauberian theorems for the \(L_{\nu,n}\) transformation.


44A15 Special integral transforms (Legendre, Hilbert, etc.)
44A10 Laplace transform