试论希尔伯特的积分方程与谱理论

On Hilbert's Integral Equation and Spectral Theory

文章探讨了蕴含在希尔伯特积分方程工作中的思想,揭示了他在分析学思想方法上做出的重大变革,进而指出该变革导致了泛函分析思想方法的产生,也指出他的谱理论在物理学上的重要应用。

This paper explores Hilbert＇s integral equation which is full of profound ideas, reveals the major revolution that he made in the thinking mode of analytics, shows that this revolution breeds the idea and method of functional analysis, and points out that his spectral theory has played an important role in physics.