论文标题
轴向谐波函数和S谱上的谐波功能演算
Axially harmonic functions and the harmonic functional calculus on the S-spectrum
论文作者
论文摘要
引入了有关S光谱的光谱理论为Quaternionic量子力学提供了适当的数学设置，但很快就意识到该理论有不同的应用，例如，对于分数热扩散以及DIRAC操作员在流派上的光谱理论。在这篇开创性的论文中，我们基于s光谱和轴向谐波函数的整体表示介绍了谐波功能演算。该积分可以看作是谐波分析与光谱理论之间的桥梁。谐波功能演算的分解运算符是伪S-Resolvent操作员的交换版本。这种新的演算也以自然的方式出现在F功能演算的产品规则中。
The spectral theory on the S-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were different applications of this theory, for example, to fractional heat diffusion and to the spectral theory for the Dirac operator on manifolds. In this seminal paper we introduce the harmonic functional calculus based on the S-spectrum and on an integral representation of axially harmonic functions. This calculus can be seen as a bridge between harmonic analysis and the spectral theory. The resolvent operator of the harmonic functional calculus is the commutative version of the pseudo S-resolvent operator. This new calculus also appears, in a natural way, in the product rule for the F-functional calculus.
