An inversion formula for the distributional generalized Laplace transformation
type: Item
instance of: scholarly article
title: An inversion formula for the distributional generalized Laplace transformation
zbMATH Open document ID: 0866.46018
author: S. K. Akhaury
author: C. S. P. Lugun
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-07-24T00:00:00Z
review text: A generalization of the classical Laplace transform \[ L[f(t);s]= \int^\infty_0 e^{-st}f(t)dt, \qquad \text{Re}(s)>0, \] was given by \textit{H. M. Srivastava} [Mathematica, Cluj 10(33), 385-390 (1968; Zbl 0176.10202)] in the form \[ S^{(\rho,\sigma)}_{q,k,m} [f(t),s]=\int^\infty_0 (st)^{\sigma-1/2} e^{-qst/2} W_{k,m}(\rho st) f(t)dt, \tag \(*\) \] where \(W_{k,m}(z)\) denotes the Whittaker function of second kind. The authors in the present paper extend to Schwartz's distribution an inversion formula for the generalized Laplace transform \((*)\).
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 902439
zbMATH Keywords: Whittaker function
zbMATH Keywords: distribution
zbMATH Keywords: abelian theorems
zbMATH Keywords: Laplace transform
zbMATH Keywords: Schwartz's distribution
zbMATH Keywords: inversion formula
zbMATH Keywords: generalized Laplace transform
reviewed by: Ravinder Krishna Raina
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0019
OpenAlex ID: W2017052324
DOI: 10.1006/JMAA.1996.0019
description: scientific article; zbMATH DE number 902439