Diracδ函数的微观分析及其应用

来源期刊：中南大学学报(自然科学版)1991年第5期

论文作者：曾君莲

文章页码：576 - 581

关键词：微观分析; 开核子; 闭核子; 像函数Heavside函数; Diracδ函数

Key words：microcosmic analysis; open kernel; closed kernel; image function; Heaviside-function; Dirac δ-function

摘    要：本文以非标准分析为工具,研究了核子上的积分与求导,并从实例出发,引出了Heaviside函数,又论证了Heaviside函数的导数就是Diracδ函数;从而给出了Diracδ函数一个精确的表示方法。之后又进一步研究了它的性质及应用。

Abstract: In this paper the author has studied differentiation and integration on akernel with the nonstanard analysis as a tool, and introduced Heaviside-function from practical examples, then proved that the derivative of Heaviside-function is just the Dirac δ-function. Therefore, an accurate expression ofδ-function is obtained. Also, the properties and application of δ-function isstudied further in this paper.