A generalization of the L2-transform and its applications

Abstract

The purpose of this paper is to generalize the Laplace-type L2 transform to the L2n-transform by introducing the number n in the formula for L2. A similar generalization P2n of the Widder potential-transform is also given. The main result is a collection of formulas linking e.g. the integral of a product of two P2n-transforms in terms of an integral of one of the functions against the the P2n-transform of the other. This equation is a kind of Parseval identity, as known from Fourier analysis. © 2016, Universitatii Al.I.Cuza din Iasi. All rights reserved.