Clifford代数Cln+1,0(C) 中的k-Hypergenic向量值函数的性质
some Properties of k-Hypergenic Functions with Vector Value in the Clifford Algebra Cln+1,0(C)

作者: 边小丽 * , 王亚萍 , 李 霞 :天津职业技术师范大学,天津;

关键词: Clifford分析k-Hypergenic向量值函数k-Hypergenic调和向量值函数Clifford Analysis k-Hypergenic Functions with Vector Value k-Hypergenic Harmonic Functions with Vector Value

摘要:
在实Clifford分析中的k-超正则向量值函数和k-超调和向量值函数定义的基础上,首先给出了复Clifford代数Cln+1,0(C) 中的k-Hypergenic向量值函数和k-Hypergenic调和向量值函数的定义,然后引入了一个偏微分方程组,借助这个偏微分方程组讨论了k-Hypergenic向量值函数的性质及其与k-Hypergenic调和向量值函数的关系,最后得到这个偏微分方程组可解性的充分必要条件。

Abstract: In this paper, on the basis of the definition of the k-Hypermonogenic and k-Hyperbolically har-monic functions with vector value in real Clifford analysis, the definition of the k-Hypergenic functions and k-Hypergenic harmonic functions with vector value in the Clifford algebra Cln+1,0(C) is given. Then, some properties of k-Hypergenic functions with vector value and their relation with k-Hypergenic harmonic functions with vector value are discussed by introducing a partial differential equation system. Furthermore, a necessary and sufficient condition for the solvability of the partial differential equation system is obtained.

文章引用: 边小丽 , 王亚萍 , 李 霞 (2016) Clifford代数Cln+1,0(C) 中的k-Hypergenic向量值函数的性质。 理论数学, 6, 464-470. doi: 10.12677/PM.2016.66063

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