右型群上的切向k-Cauchy-Fueter算子及其Bochner-Martinelli型公式

IF 1.1 2区 数学 Q2 MATHEMATICS, APPLIED
Yun Shi, Guangzhen Ren
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引用次数: 0

摘要

k-柯西–富特算子和切向k-柯西-富特算子分别是几个复变量理论中柯西–黎曼算子和切向柯西–黎曼算子的四元数对应物。王在《关于k—柯西—富特复形的边界复形,arXiv:221013656》一文中引入了右型群的概念,它具有第二步幂零李群的结构,四元数分析的许多方面都可以推广到这类群。本文将右型群推广到任何第二步情形,并引入Cauchy–Fueter算子在\({\mathbb{H}}^n \times{\math bb{R})^R上的推广。然后,我们在分层右型群上建立了切向k-Cauchy-Fueter算符的Bochner–Martinelli型公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula

The k-Cauchy–Fueter operator and the tangential k-Cauchy–Fueter operator are the quaternionic counterpart of Cauchy–Riemann operator and the tangential Cauchy–Riemann operator in the theory of several complex variables, respectively. In Wang (On the boundary complex of the k-Cauchy–Fueter complex, arXiv:2210.13656), Wang introduced the notion of right-type groups, which have the structure of nilpotent Lie groups of step-two, and many aspects of quaternionic analysis can be generalized to this kind of group. In this paper we generalize the right-type group to any step-two case, and introduce the generalization of Cauchy–Fueter operator on \({\mathbb {H}}^n\times {\mathbb {R}}^r.\) Then we establish the Bochner–Martinelli type formula for tangential k-Cauchy–Fueter operator on stratified right-type groups.

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来源期刊
Advances in Applied Clifford Algebras
Advances in Applied Clifford Algebras 数学-物理:数学物理
CiteScore
2.20
自引率
13.30%
发文量
56
审稿时长
3 months
期刊介绍: Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.
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