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 Cl_n+1,0(C)

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Cl_n+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 Cl_n+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.