distributional differentiation and integration
Stieltjes transforms and quasiasymptotic behavior on new generalized functions
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].
scientific article; zbMATH DE number 1670994