On the generalized convolution for I-transform
type: Item
instance of: scholarly article
title: On the generalized convolution for I-transform
zbMATH Open document ID: 1055.44007
author: Nguyen Xuan Thao
author: Trinh Tuan
published in: Acta Mathematica Vietnamica
publication date: 2004-06-18T00:00:00Z
review text: The authors introduce the so-called \(I\)-transform, which generalizes integral transformations with the Meijer \(G\)-functions and the Fox \(H\)-functions as kernels. It can be written also in terms of the Mellin-Barnes integral. A generalized convolution is constructed for this transformation basing on the hypergeometric approach [see, for instance, in the monograph of \textit{S. B. Yakubovich} and \textit{Y. F. Luchko}, The hypergeometric approach to integral transforms and convolutions (Mathematics and its Applications 287, Kluwer, Dordrecht) (1994; Zbl 0803.44001)]. General theorems of the existence and mapping properties for this convolution are exhibited. Various examples of the method are given. It includes convolutions with the Bessel functions and the parabolic cylinder functions.
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33C60
zbMATH DE Number: 2076047
zbMATH Keywords: convolution
zbMATH Keywords: Laplace transform
zbMATH Keywords: Mellin transform
zbMATH Keywords: Bessel functions
zbMATH Keywords: Fox \(H\)-function
zbMATH Keywords: Meijer \(G\)-function
zbMATH Keywords: Mellin-Barnes integral
zbMATH Keywords: \(I\)-transform
reviewed by: S. Yakubovich
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2076047