施瓦兹分布概念的形成

The formation of the concept of the L. Schwartz's distribution

通过原始文献考证对古典函数概念进行推广的方法。探究了施瓦兹引入分布概念的原因和过程,以及函数、测度、分布和广义函数概念之间的关系。指出由于自然科学的需求以及对对偶空间的深刻理解,施瓦兹在1945年4月成功引入了分布概念。分布是对古典函数和测度概念的推广,是广义函数的一种。

Based on the methods of ＂ Why Mathematics＂ and researching the primary materials, this paper discusses reasons and the process that Schwartz introduced the concept of distribution and the relations about function, measure, distribution and generalized function. This paper concludes that for the requirement of natural science and the deeply understanding of the dual space, Schwartz introduced the concept of distribution in April 1945. The distribution generalizes the concept of function and it is a kind of the generalized function.