A new theory of generalized functions
type: Item
instance of: scholarly article
title: A new theory of generalized functions
zbMATH Open document ID: 0715.46015
published in: Moscow University Mathematics Bulletin
publication date: 1989-01-01T00:00:00Z
review text: Let \(\Omega\) be the domain in \({\mathbb{R}}^ n\). In this paper the new space of generalized functions \({\mathcal G}(\Omega)\) is defined as follows: Consider the space of infinite differentiable functions defined on (0,1)\(\times \Omega\). Two functions are called equivalent, if they coincide on the set (0,\(\epsilon\))\(\times \Omega\) for some positive \(\epsilon\). The generalized function space \({\mathcal G}(\Omega)\) is the quotient space of the above space with respect to this equivalence relation. The space of Schwartz distributions \({\mathcal D}'(\Omega)\) is imbedded in the space \({\mathcal G}(\Omega)\) and an operation of multiplication for elements of \({\mathcal G}(\Omega)\) is determined [see also \textit{M. S. Burgin}, Dokl. Akad. Ukrain. SSR, Ser. A 1987, No.7, 5-9 (1987; Zbl 0628.46037)]. The author states that the new theory of distributions describe more adequately physical reality and gives opportunity to define the generalized solution for some equations, what is impossible in classical theory.
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 4177883
zbMATH Keywords: new space of generalized functions
zbMATH Keywords: space of Schwartz distributions
zbMATH Keywords: multiplication
author: Yu V. Egorov
reviewed by: D. Zarnadze
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4177883