本文選題：施瓦茲空間 + 傅里葉變換��； 參考：《自然辯證法通訊》2017年03期

【摘要】：施瓦茲的分布理論是泛函分析的重要組成部分,而施瓦茲空間是分布理論中的核心空間之一。文章探究施瓦茲空間誕生的原因,揭示出施瓦茲想利用傅里葉變換來尋找卷積方程的一般求解策略,進而在研究分布的傅里葉變換的驅動之下引進了施瓦茲空間。對施瓦茲空間引入的緣由進行探究體現(xiàn)出高度抽象的純粹數(shù)學不但沒有脫離實際,反而來源于實際。同時,施瓦茲求解卷積方程的策略中蘊含著分析代數(shù)化的思想,這一思想為進行數(shù)學研究提供了一種可資借鑒的思路。
[Abstract]:Schwartz's distribution theory is an important part of functional analysis, and Schwartz space is one of the core spaces in distribution theory. This paper explores the causes of the birth of Schwartz space, reveals that Schwartz wants to use Fourier transform to find the general solution strategy of convolution equation, and then introduces Schwartz space driven by the study of distributed Fourier transform. Exploring the causes of the introduction of Schwartz space shows that pure mathematics, which is highly abstract, does not deviate from reality, but comes from reality. At the same time, Schwaz's strategy for solving convolution equations contains the idea of algebraic analysis, which provides a useful method for mathematical research.
【作者單位】： 西安石油大學理學院;西北大學數(shù)學與科學史研究中心;
【基金】：國家自然科學基金資助項目(項目編號:11571276;11501444)
【分類號】：K835.65;O177
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本文編號：2053091