非标准δ函数的研究

STUDY OF THE NONSTANDARD δ FUNCTIONS

按着[1]对应于Schwartz理论意义下的每个广义函数,有个Q广义函数,它是非标准函数的一个特殊类。和作为广义函数的Diracδ函数相对应的Q广义函数,其中的非标准函数都是非标准δ函数。本文提出了非标准δ函数的某些重要性质,得到了一个判定Q_0中的非负函数是否为非标准δ函数的判别准则。

In [1], to every distribution in the sense of the theory of Schwartz there corre sponds a Q--distribution, which is a particular class of nonstandard functions. To the dirac δ function as a distribution there corresponds the Q--distribution in which nonstandard functions are all nonstandard δ functions. This paper provides some important properties of nonstandard δ functions, then, by Theorem 3, we have obtained the criterion that can verify whether anon--negative function in Q_0 is nonstandard δ function.