| 谢永红.Clifford分析中对偶的$k$-Hypergenic函数[J].数学年刊A辑,2014,35(2):235~246 |
| Clifford分析中对偶的$k$-Hypergenic函数 |
| Dual k-Hypergenic Functions in Clifford Analysis |
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| DOI： |
| 中文关键词: 对偶的$k$-hypergenic函数,Cauchy积分公式,实Clifford 分析 |
| 英文关键词:Dual $k$-hypergenic function, Cauchy integral formula, Real Clifford analysis |
| 基金项目:国家自然科学基金 (No.11301136, No.11101139),
河北省自然科学基金(No.A2014205069) 和浙江省自然科学基金 (No.Y6090036, No.Y6100219) |
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| 中文摘要: |
| 研究了取值于实Clifford代数空间$Cl_{n+1,0}(\mathbb{R})$
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
$U\backslash{\partial \Omega_2}$中对偶的hypergenic函数. |
| 英文摘要: |
| In this paper, dual $k$-hypergenic functions with values in a real Clifford algebra space
$Cl_{n+1,0}(\mathbb{R})$ 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 $U\backslash{\partial \Omega_2}$. |
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