Clifford分析中双Hypergenic函数的等价条件

The Equivalent Conditions of Bihypergenic Functions in Clifford Analysis

摘要: 本文首先以双hypergenic函数的定义为基础，借助Cl_n+1,0(R)空间中的一种分解，讨论了Cl_n+1,0(R)中双hypergenic函数的一个等价条件，其与复分析中的Cauchy-Riemann方程比较类似，其次通过对结果中方程的某些量进行变换得到了双hypergenic函数的又一个等价刻画，这些等价条件建立了双hypergenic函数与偏微分方程之间的联系，使Clifford分析的函数理论有了进一步发展，对于研究高维空间中的方程和算子提供了理论基础。

Abstract: In this paper, based on the definition of bihypergeneric function, we first discuss an equivalent condition of the bihypergenic function in Cl_n+1,0(R) by a decomposition in Cl_n+1,0(R) space, which is similar to the Cauchy-Riemann equation in complex analysis. Second, by changing some quantities of the equations in the results, we obtain another equivalent characterization of the bihypergenic function, which establishes the relation between the bihypergenic function and the partial differential equation functions. They further develop the function theory of Clifford analysis and provide a theoretical basis for the study of equations and operators in high-dimensional space.