| 谢永红,杨贺菊.复Clifford分析中的复$k$-Hypergenic 函数[J].数学年刊A辑,2013,34(2):211~222 |
| 复Clifford分析中的复$k$-Hypergenic 函数 |
| Complex $k$-Hypergenic Functions in Complex Clifford Analysis |
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| DOI： |
| 中文关键词: 复$k$-hypergenic函数, 复$k$-hypergenic调和函数, 复Clifford 分析 |
| 英文关键词:Complex $k$-hypergenic function,
Complex $k$-hypergenic harmonic function, Complex Clifford analysis |
| 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) |
| Author Name | Affiliation | E-mail | | 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. | 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. | xyh1973@126.com | | College of Science, Hebei University of Science and Technology, Shijiazhuang
050018, China. | College of Science, Hebei University of Science and Technology, Shijiazhuang
050018, China. | earnestqin7384@sina.com |
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| 中文摘要: |
| 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$P_0f(z)=u(z)$. |
| 英文摘要: |
| 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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