Clifford代数Cl_n+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[1] 王亚萍[1] 李霞 

机构地区：[1]天津职业技术师范大学,天津

出　　处：《理论数学》2016年第6期464-470,共7页Pure Mathematics

基　　金：国家自然科学基金数学天元基金(11226086,11526154);国家自然科学基金(11601390);国家自然科学基金面上项目(11472298);天津职业技术师范大学校级项目(KJ14-30)。

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。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.

关 键 词：CLIFFORD分析 k-Hypergenic向量值函数 k-Hypergenic调和向量值函数 

分 类 号：O1[理学—数学]