Nonstandard theories of generalised functions (Q2754351)

Laurent Schwartz's theory (given in 1950) has been explored over the years through alternative approaches and has been expanded by the introduction of several types of generalised distributions. The introduction of Nonstandard analysis made it possible to unify and simplify the treatment of the Schwartz's theory.NEWLINENEWLINENEWLINEThe present paper gives an extension of the approach, suggested by Sebastiao e Silva axioms for Schwartz distributions, applied to the theory of Sato hyperfunctions. One may (for interesting reading of the paper) refer to [\textit{R. F. Hoskins} and \textit{J. Sousa Pinto}, J. Port. Math. 48, 195-216 (1991; Zbl 0765.46060) and Proc. Indian Acad. Sci. Math. Sci. 109, 389-395 (1999; Zbl 0846.46037)]. Section 2 of this paper gives relevant logics and definitions of distributions, Silva axioms, ultradistributions and presents the analysis for predistributions and the analysis for predistributions of finite and infinite orders.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00008].