首页 | 本学科首页   官方微博 | 高级检索  
     检索      

Clifford分析中对偶的k-Hypergenic函数
引用本文:谢永红.Clifford分析中对偶的k-Hypergenic函数[J].数学年刊A辑(中文版),2014,35(2):235-246.
作者姓名:谢永红
作者单位:河北师范大学数学与信息科学学院, 石家庄 050024; 中国科学技术大学数学科学学院, 合肥 230026.
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)
摘    要: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.

关 键 词:对偶的$k$-hypergenic函数  Cauchy积分公式  实Clifford  分析

Dual k-Hypergenic Functions in Clifford Analysis
XIE Yonghong.Dual k-Hypergenic Functions in Clifford Analysis[J].Chinese Annals of Mathematics,2014,35(2):235-246.
Authors:XIE Yonghong
Institution:College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China; School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China.
Abstract: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 $U\backslash{\partial \Omega_2}$.
Keywords:Dual  $k$-hypergenic function    Cauchy integral formula  Real Clifford analysis
本文献已被 CNKI 等数据库收录!
点击此处可从《数学年刊A辑(中文版)》浏览原始摘要信息
点击此处可从《数学年刊A辑(中文版)》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号