| k—正则函数及某些边值问题 |
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| 引用本文： | 杨丕文. k—正则函数及某些边值问题[J]. 四川师范大学学报(自然科学版), 2001, 24(1): 5-8 |
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| 作者姓名： | 杨丕文 |
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| 作者单位： | 四川师范大学 数学系, |
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| 摘 要： | 研究k-正则函数u(z)(k阶方程δ^k/δz^-^k u=0的解）。讨论了k-正则函数的若干函数论性质和获得了非齐次k阶方程δ^k/δz^-^k u=f的积分形式的特解，证明了以上两类函数及k调和函数的Dirichlet边值问题的解是存在唯一的。
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| 关 键 词： | K－正则函数 解析函数 K调和函数 DIRICHLET边值 |
| 文章编号： | 1001-8395（2001）01-0005-04 |
| 修稿时间： | 2000-01-19 |
The k-Regular Function andSome Boundary Value Problems |
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| YANG Pi-wen. The k-Regular Function andSome Boundary Value Problems[J]. Journal of Sichuan Normal University(Natural Science), 2001, 24(1): 5-8 |
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| Authors: | YANG Pi-wen |
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| Abstract: | In this paper, k-regular function (the solution of the k order equation kku=0) is studied. It is proved that the k-regular function can be uniquely represented by analytic functions, some function theoretic properties of the k-regular function and the integral representation of the solution of the inhomogeneous equation kku=f are obtained. Moreover, it is also proved that solutions of the Dirichlet boundary value problems for above two classes of functions and the k-harmonic function uniquely exist. |
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| Keywords: | k-regular function Analytic function k-harmonic function Dirichlet boundary value problem@ |
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