中文摘要：

施瓦兹的分布理论是泛函分析的重要组成部分,而施瓦兹空间是分布理论中的核心空间之一。文章探究施瓦兹空间诞生的原因,揭示出施瓦兹想利用傅里叶变换来寻找卷积方程的一般求解策略,进而在研究分布的傅里叶变换的驱动之下引进了施瓦兹空间。对施瓦兹空间引入的缘由进行探究体现出高度抽象的纯粹数学不但没有脱离实际,反而来源于实际。同时,施瓦兹求解卷积方程的策略中蕴含着分析代数化的思想,这一思想为进行数学研究提供了一种可资借鉴的思路。

英文摘要：

Schwartz＇s distribution theory is an important part of functional analysis, and Schwartz space is one of the most centre spaces in distributions theory. The purpose of this paper is to discuss the reason about creating the Schwartz space. This paper concludes that Schwartz would like to use Fourier transformation to solve convolution equation. He introduced the Schwartz space in order to study the Fourier transformation of distributions. And that implies that the pure mathematical theory isn＇t far away from practical issue, but keep close touch with it. Furthermore, Schwartz＇s methods contain the idea about transforming analytical problems into algebra, which give us a thought to study mathematics.