On the problem of constructing integral transforms by means of composition technique
type: Item
instance of: scholarly article
title: On the problem of constructing integral transforms by means of composition technique
zbMATH Open document ID: 0832.44004
published in: Russian Mathematics
publication date: 1995-12-14T00:00:00Z
review text: Along with classical transforms, such as Fourier, Mellin, Hankel, and those of convolution type, the modern investigations use integral transforms with respect to subscripts, such as Kantorovich-Lebedev's transform, Mehler-Fock's, Lebedev-Skal'skaya's, and other ones. By means of representation of integral transforms as compositions of known transforms and due to properties of the latter ones, in the present article we prove for the first time the composition theorems of Plancherel type for subscript transforms. We extend the composition method on Watson's general transforms and construct new integral transforms with respect to subscript of the Lommel function and of some parameters of Meijer's \(G\)-function.
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 819999
zbMATH Keywords: convolution
zbMATH Keywords: integral transforms
zbMATH Keywords: Kantorovich-Lebedev's transform
zbMATH Keywords: composition theorems of Plancherel type
zbMATH Keywords: subscript transforms
zbMATH Keywords: Watson's general transforms
zbMATH Keywords: Lommel function
zbMATH Keywords: Meijer's \(G\)-function
author: S. Yakubovich
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 819999