Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions

IF 0.3 Q4 MATHEMATICS
F. Vasilescu
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引用次数: 2

Abstract

Abstract 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 also 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.
基于干函数的Clifford算子的谱与解析泛函演算
摘要本文的主要目的是构造Clifford算子的解析泛函演算,Clifford算子是作用于Clifford代数上的某些模上的算子。与其他作者之前的一些工作不同,我们使用复平面上定义的谱,以及在该谱的邻域上解析的某些干函数。由于柯西变换的同构性,使得在Clifford代数中有值的切片正则函数用解析干函数代替成为可能。本文第一部分证明了柯西变换的存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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