积分变换中卷积的微分性质  

Differential Properties of Convolution in Integral Transform

作　　者：马纪英[1] 王潮[1] 姜文鹏 MA Jiying;WANG Chao;JIANG Wenpeng(Shijiazhuang Posts and Telecommunications Technical College, Shijiazhuang Hebei 050021, China)

机构地区：[1]石家庄邮电职业技术学院

出　　处：《长沙大学学报》2019年第5期10-12,共3页Journal of Changsha University

摘　　要：卷积是积分变换的一种重要方法,尤其是在求函数的逆变换和积分值,以及线性系统的分析中具有重要作用.文章从介绍卷积的概念和微分性质入手,引入多元积分的积分上限函数作为基础,利用它的求导性质对卷积的微分性质进行了证明,最后给出了卷积方法在积分变换逆变换和微分积分方程中的应用实例.Convolution is an important method of integral transformation, especially in the analysis of inverse transformation and integral value of functions and linear systems. This paper begins with the introduction of the concept and differential properties of convolution, introduces the integral upper bound function of multivariate integral as the basis, proves the differential properties of convolution by its derivative properties, and finally gives the examples of applying convolution method in inverse transformation of fractional transformation and differential integral equation.

关 键 词：卷积 微分性质 证明 

分 类 号：O172[理学—数学]