| 复Clifford分析中的复$k$-Hypergenic 函数 |
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| 引用本文： | 谢永红,杨贺菊.复Clifford分析中的复$k$-Hypergenic 函数[J].数学年刊A辑(中文版),2013,34(2):211-222. |
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| 作者姓名： | 谢永红 杨贺菊 |
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| 作者单位： | 中国科学技术大学数学科学学院, 合肥 230026; 河北师范大学数学与信息科学学院, 石家庄 050024.;河北科技大学理学院, 石家庄 050018. |
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| 基金项目： | 国家自然科学基金 (No.11101139), 浙江省自然科学基金项目(No.Y6090036, No.Y6100219)和河北师范大学一般基金(No.L2009y02) |
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| 摘 要： | 首先给出了复$k$-hypergenic函数的几个等价条件,其中包括广义的Cauchy-Riemann方程.其次给出了复$k$-hypergenic调和函数的几个等价条件.
最后讨论了复$k$-hypergenic函数和复$k$-hypergenic调和函数的关系.例如,已知一个复$k$-hypergenic调和函数$u(z)$,则局部存在复$k$-hypergenic
函数$f(z)$, 使得$P_0f(z)=u(z)$.
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| 关 键 词： | 复$k$-hypergenic函数 复$k$-hypergenic调和函数 复Clifford 分析 |
Complex $k$-Hypergenic Functions in Complex Clifford Analysis |
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| School of Mathematical Sciences,University of Science and Technology of
Chin,Hefei,China; College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang,China. and College of Science,Hebei University of Science and Technology,Shijiazhuang,China..Complex $k$-Hypergenic Functions in Complex Clifford Analysis[J].Chinese Annals of Mathematics,2013,34(2):211-222. |
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| Authors: | School of Mathematical Sciences University of Science and Technology of
Chin Hefei China; College of Mathematics and Information Science Hebei Normal University Shijiazhuang China and College of Science Hebei University of Science and Technology Shijiazhuang China |
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| Institution: | School of Mathematical Sciences, University of Science and Technology of
China, Hefei 230026, China; College of Mathematics and Information Science,
Hebei Normal University, Shijiazhuang 050024, China.;College of Science, Hebei University of Science and Technology, Shijiazhuang
050018, China. |
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| Abstract: | Firstly, some equivalent conditions of complex $k$-hypergenic functions are obtained, one of which is the generalized Cauchy-Riemann equation.
Then, some equivalent conditions of complex $k$-hypergenic harmonic functions are obtained.
Finally, the relationships between complex $k$-hypergenic functions and complex $k$-hypergenic harmonic functions are given. For example, for a given
complex $k$-hypergenic harmonic function $u(z)$, there locally exists a complex $k$-hypergenic function $f(z)$ such that $P_0f(z)=u(z)$. |
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| Keywords: | Complex $k$-hypergenic function Complex $k$-hypergenic harmonic function Complex Clifford analysis |
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