Iterated Stieltjes transform of generalized functions
type: Item
instance of: scholarly article
title: Iterated Stieltjes transform of generalized functions
zbMATH Open document ID: 0586.46036
DOI: 10.1155/S0161171285000461
author: Lakshmi Shanker Dube
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46030
review text: The generalized \(S_ 2\)-transform of a member of f of a certain space of generalized functions is defined as \(F(x)=<f(t),K(x,t;\rho)>\), where \[ K(x,t;\rho)=\int^{\infty}_{0}\frac{1}{(x+y)^{\rho}(y+t)^{\rho}}dy, \quad \rho >1/2,\quad 0<x<\infty \quad and\quad 0<t<\infty. \] An inversion theorem for the transform is established interpreting the convergence in the weak distributional sense.
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 3939995
zbMATH Keywords: iterated Stieltjes transform
zbMATH Keywords: generalized \(S_ 2\)-transform
zbMATH Keywords: space of generalized functions
zbMATH Keywords: inversion theorem
zbMATH Keywords: convergence in the weak distributional sense
MaRDI profile type: Publication
OpenAlex ID: W2008775068
description: scientific article; zbMATH DE number 3939995