论文标题
Clifford操作员通过STEM函数的频谱和分析功能演算
Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions
论文作者
论文摘要
这项工作的主要目的是为Clifford操作员建造分析功能演算，该计算是在Clifford代数上作用于某些模块的操作员。与其他作者的某些上一部作品不同，我们使用在复杂平面中定义的频谱以及某些茎功能，在这种频谱的邻里中进行分析。通过分析词干函数在Clifford代数中具有值的切片常规函数的替换是可能的，这是可能的，这是由于由Cauchy型变换引起的同构，其存在在本工作的第一部分中得到了证明。
The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a spectrum defined in the complex plane, and certain stem functions, analytic in neighborhoods of such a spectrum. The replacement of the slice regular functions, having values in a Clifford algebra, by analytic stem functions becomes possible because of an isomorphism induced by a Cauchy type transform, whose existence is proved in the first part of this work.
