[D, φ(x), λ]=0 的充分必要条件

廖建全, 李兴民

数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1085-1090.

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数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1085-1090. DOI: 10.12386/A2009sxxb0136
论文

[D, φ(x), λ]=0 的充分必要条件

    廖建全1, 李兴民2
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The Necessary and Sufficient Condition for [D, φ(x), λ]=0

    Jian Quan LIAO1, Xing Min LI2
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摘要

设Dirac算子 , . 若 , 则称 为左 -解析函数. 本文证明了, 若 , 则对一切常数 的充分必要条件是 为Stein--Weiss共轭调和函数系.  

Abstract

Let be the Dirac operator, . If , then is called a left -analytic function. In this paper, we prove that if , then for all if and only if is the Stein--Weiss conjugate harmonic system.  

关键词

八元数 / O-解析函数 / Stein--Weiss共轭调和函数系

Key words

Octonions / O-analytic function / Stein--Weiss conjugate harmonic system

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廖建全, 李兴民. [D, φ(x), λ]=0 的充分必要条件. 数学学报, 2009, 52(6): 1085-1090 https://doi.org/10.12386/A2009sxxb0136
Jian Quan LIAO, Xing Min LI. The Necessary and Sufficient Condition for [D, φ(x), λ]=0. Acta Mathematica Sinica, Chinese Series, 2009, 52(6): 1085-1090 https://doi.org/10.12386/A2009sxxb0136

参考文献



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[8] Stein E. M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton: Princeton Univ. Press, 1971.



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基金

国家教委博士点基金资助项目(20050574002)

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