D(φ(εx))=0的充分必要条件

廖建全, 王晋勋

数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 597-604.

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数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 597-604. DOI: 10.12386/A2013sxxb0060
论文

D(φ(εx))=0的充分必要条件

    廖建全1, 王晋勋2
作者信息 +

The Necessary and Sufficient Condition for D(φ(εx))=0

    Jian Quan LIAO1, Jin Xun WANG2
Author information +
文章历史 +

摘要

设Dirac算子为定义在一非空开集Ω ⊂ R8上的八元数值函数. 本文证明了,对一切常数ε ∈ O,D(φ(εx))=0的充分必要条件是φ为Ω上的Stein-Weiss解析函数.

Abstract

Let be the Dirac operator and let φ(x) be an octonionvalued function defined in a non-empty open set Ω ⊂ R8. In this paper, we prove that D(φ(εx))=0 for all ε ∈ O if and only if φ is a Stein-Weiss analytic function in Ω.

关键词

八元数 / O-解析函数 / Stein-Weiss解析函数

Key words

octonions / O-analytic function / Stein-Weiss analytic function

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廖建全, 王晋勋. D(φ(εx))=0的充分必要条件. 数学学报, 2013, 56(4): 597-604 https://doi.org/10.12386/A2013sxxb0060
Jian Quan LIAO, Jin Xun WANG. The Necessary and Sufficient Condition for D(φ(εx))=0. Acta Mathematica Sinica, Chinese Series, 2013, 56(4): 597-604 https://doi.org/10.12386/A2013sxxb0060

参考文献

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基金

广东第二师范学院2012年博士科研专项经费研究项目资助(2012AFR03)
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