希尔伯特空间诞生探源

A Historical Survey:The birth of Hilbert space

希尔伯特空间是泛函分析和量子力学的核心内容。希尔伯特空间思想起源于希尔伯特的积分方程工作,这一思想很快由他的追随者给出了具体形式,应量子力学发展的需要,并顺应20世纪结构数学发展的潮流,冯.诺依曼用公理化定义了抽象希尔伯特空间。对希尔伯特空间的起源及形成过程进行研究可以使我们更好地理解希尔伯特空间理论和泛函分析的历史发展过程,同时也为揭示数学与物理之间的联系提供了一个重要视角。

Hilbert space is an important content of functional analysis and quantum mechanics. The idea of Hilbert space stems from Hilbert＇s works on integral equation, but soon was given concrete forms by Hilbert＇ s followers. To satisfy the need for the development of quantum mechanics and fol- low the trend of development of structural mathematics in the 20th century, John van Neumann defined abstract Hilbert space axiomatically. The his- torical exploring on the origin and evolution of Hilbert space not only help us to better understand the theory of Hilbert space and the history of func- tional analysis, but also provide a significant perspective to reveal the links between mathematics and physics.