施瓦茲空間(Schwarz space)又稱急降函式空間,是一類光滑函式空間。施瓦茲創建的分布理論是泛函分析的又一重要進展,而施瓦茲空間是分布理論中的一類重要基本函式空間。它的引入是實際需要的驅動,而並非是為了純粹數學理論的發展與完善。為了求解卷積方程,施瓦茲通過傅立葉變換將其轉化為乘積方程。這就需要定義分布的傅立葉變換,進而他引入了施瓦茲空間,從而解決了卷積方程的求解問題。他的這一研究策略蘊含著分析代數化的思想,這為做數學研究提供了一種可資借鑑的思路。這一策略也揭示出高度抽象的純粹數學不但沒有脫離實際,反而與實際問題有著密不可分的關係,而這也正是20世紀數學發展的特徵之一。施瓦茲的這一工作豐富了廣義函式理論,發展了經典的傅立葉變換,求解了卷積方程,給出了研究線性偏微分方程的新思路。
基本介紹
- 中文名:施瓦茲空間
- 外文名:Schwarz space
- 別名:急降函式空間
- 屬性:一類光滑函式空間
- 提出者:施瓦茲
- 相關概念:傅立葉變換、卷積方程等
定義
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施瓦茲空間上傅立葉變換的重要性質
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