δ函数的定义及其性质  

The definition for δ function and its properties

作　　者：闵琦[1] 

机构地区：[1]红河学院教务处,云南蒙自661100

出　　处：《大学物理》2004年第9期18-20,共3页College Physics

摘　　要：对δ函数的传统定义及由此引起的奇性展开讨论,说明了在经典意义下δ函数可以被看成是弱收敛函数序列的弱极限以及阶跃函数Heaviside函数的导数;最后,借用泛函分析中广义函数的概念给出了δ函数的严格数学定义,并就其性质进行了讨论.Through discussing the conventional definition of δ function and the strange qualities thus induced, it is pointed out that δ function can be understood as the weak limit of weak convergent functions and the derivative of Heaviside function traditionally. Moreover, the strict definition of δ function is given with the conception of generalized function in functional analysis, and the properties of δ function are discussed as well.

关 键 词：Δ函数 弱极限 Heaviside函数 广义函数 

分 类 号：O411.1[理学—理论物理]