Clifford分析中对偶的k-Hypergenic函数

Dual k-Hypergenic Functions in Clifford Analysis

研究了取值于实Clifford代数空间Cl_(n+1,0)(R)中对偶的k-hypergenic函数.首先,给出了对偶的k-hypergenic函数的一些等价条件,其中包括广义的Cauchy-Riemann方程.其次,给出了对偶的hypergenic函数的Cauchy积分公式,并且应用其证明了(1-n)-hypergenic函数的Cauchy积分公式.最后,证明了对偶的hypergenic函数的Cauchy积分公式右端的积分是U\Ω_2中对偶的hypergenic函数.

In this paper, dual k-hypergenic functions with values in a real Clifford algebra space Cln＋1,0（R） are discussed. First, some equivalent conditions of dual k-hypergenic functions are given, one of which is the generalized Cauchy-Riemann equation. Then, Cauchy integral formula for dual hypergenic functions is given and as an application of it, Cauchy integral formula for （1-n）-hypergenic functions is proved. Finally, it is proved that the integral on the right-hand side of Cauchy integral formula for dual hypergenic functions is still a dual hypergenic function in U／σΩ2.