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k—正则函数及某些边值问题
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.
作者姓名:杨丕文
作者单位:四川师范大学 数学系,
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。

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年1月19日

The k-Regular Function and Some Boundary Value Problems
YANG Pi-wen.The k-Regular Function and Some Boundary Value Problems[J].Journal of Sichuan Normal University(Natural Science),2001,24(1):5-8.
Authors:YANG Pi-wen
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.
Keywords:k-regular function  Analytic function  k-harmonic function  Dirichlet boundary value problem@
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