论文标题
光谱定理的功能性演算方法
The Functional Calculus Approach to the Spectral Theorem
论文作者
论文摘要
提出了针对光谱定理的一致的功能演算方法，用于在希尔伯特空间上强烈通向正常运算符。与使用投影值衡量标准或乘法算子的常见方法相反，此处的功能性演算不是将其视为下属，而是将其视为中心概念。基于“可测量功能演算”的五个简单公理，该结石的理论详细开发了，包括光谱理论，独特性结果和构造原理。最后，陈述和证明了光谱定理的功能性演算形式，并讨论了一些证明变体。
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators, here the functional calculus is not treated as a subordinate but as the central concept. Based on five simple axioms for a "measurable functional calculus", the theory of such calculi is developed in detail, including spectral theory, uniqueness results and construction principles. Finally, the functional calculus form of the spectral theorem is stated and proved, with some proof variants being discussed.
