A mathematical interpretation of Dirac's \(\delta\) function
type: Item
instance of: scholarly article
title: A mathematical interpretation of Dirac's \(\delta\) function
zbMATH Open document ID: 0609.46016
DOI: 10.1007/BF01877401
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1981-01-01T00:00:00Z
review text: The two conditions \[ (1)\quad \delta (x)=0,\quad for\quad x\neq 0,\quad (2)\quad \int^{+\infty}_{-\infty}\delta (x)dx=1 \] of the Dirac \(\delta\) function are inconsistent in standard analysis. In this paper, the author began by studying the integral of the functions on the nucleon \(\alpha\) (0), and then, making use of the point function in infinitesima analysis to define the Dirac \(\delta\) function \(\delta\) (x) so that it satisfies the condition (2) and \(\delta (x)=0\), for \(x\in R\) and \(x\neq 0.\) Some various examples of Dirac \(\delta\) functions have been presented and some properties of the \(\delta\) function have been derived.
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46S20
zbMATH DE Number: 3985917
zbMATH Keywords: nucleon
zbMATH Keywords: infinitesima analysis
author: Jinru Wang
MaRDI profile type: Publication
cites work: Q5785884
cites work: Truth with Respect to an Ultrafilter or How to Make Intuition Rigorous
cites work: Dirac Delta Functions Via Nonstandard Analysis
full work available at URL: https://doi.org/10.1007/bf01877401
OpenAlex ID: W1972218875
description: scientific article; zbMATH DE number 3985917