泛函分析的历史:从沃尔泰拉到冯·诺伊曼
The History of Functional Analysis:From Vito Volterra to John von Neumann
李亚亚 1李斐2
作者信息
- 1. 西安财经大学数学学院,西安 710100
- 2. 西安石油大学理学院,西安 710065
- 折叠
摘要
泛函分析是用代数和几何的观念和方法研究分析学问题的一门学科.沃尔泰拉在泛函理论方面的工作为弗雷歇创立抽象度量空间理论奠定了先决条件,他也最早揭示出积分方程与线性方程组之间暗含的类似性.弗雷德霍姆成功将线性方程组理论推广到连续核积分方程上,成为用代数的观念和方法解决分析学问题的成功案例,这启发了希尔伯特分析与代数统一框架的构建.顺应20世纪数学抽象化发展的趋势,希尔伯特的追随者们引入几何观念,在重新表述和发展希尔伯特积分方程思想的过程中建立了泛函分析这门学科.
Abstract
Functional analysis is a subject which uses algebraic and geometric ideas and methods to study problems in analytics.Volterra's work on functional theory laid the prerequisites for Fréchet's creation of the theory of abstract metric spaces.Volterra was also the first to reveal the implied similarity between integral equations and systems of linear equations.Fredholm's successful extension of the theory of systems of linear equations to continuous kernel integral equations was a successful example of the use of algebraic ideas and methods to solve analytic problems,which inspired the construction of Hilbert's framework for the unification of analysis and algebra.In line with the trend towards abstraction in mathematics in the 20th century,Hilbert's followers introduced geometric concepts and established functional analysis in the reformulation and development of the idea of Hilbert's integral equations.
关键词
近现代数学史/泛函分析/积分方程/变分法/线性方程组Key words
history of modern mathematics/functional analysis/integral equation/calculus of variations/linear system of equations引用本文复制引用
基金项目
国家自然科学基金资助项目(12301002)
陕西省自然科学青年基金资助项目(2021JQ-763)
出版年
2024
NETL
NSTL
万方数据