Stieltjes transforms and quasiasymptotic behavior on new generalized functions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1012.46051
publication date: 2003-06-29T00:00:00Z
Mathematics Subject Classification ID: 46F30
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 42A38
zbMATH DE Number: 1670994
zbMATH Keywords: new generalized functions
zbMATH Keywords: distributional differentiation and integration
zbMATH Keywords: Stieltjes transform
author: John Schmeelk
MaRDI profile type: Publication
title: Stieltjes transforms and quasiasymptotic behavior on new generalized functions
review text: This paper presents an extension of the notion of a new generalised function (NGF for short) studied by Colombeau in the 1980s. It contains many new important discoveries.NEWLINENEWLINENEWLINEThe approach is purely algebraic; an NGF has an equivalence class of special functions representing it. Colombeau has introduced the multiplication and integration within these eigenvalue classes. Here, the author introduces a Stieltjes transform on these equivalence classes in much the same way as Colombeau introduced the Fourier transform.NEWLINENEWLINENEWLINERelevant definitions and examples cited in the paper make it self-contained.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00008].
reviewed by: P. K. Banerji
description: scientific article; zbMATH DE number 1670994