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| Koch曲线所围区域内的一类解析函数边值问题 | |
| 引用本文： | 阮正顺,罗艾花,王小林.Koch曲线所围区域内的一类解析函数边值问题[J].数学的实践与认识,2011,41(12). |
| 作者姓名： | 阮正顺 罗艾花 王小林 |
| 作者单位： | 1. 武汉工程大学理学院智能机器人湖北省重点实验室,湖北武汉,430073 2. 中南民族大学数学与统计学学院,湖北武汉,430073 3. 武汉大学数学与统计学院,湖北武汉,430072 |
| 摘 要： | 在经典解析函数边值理论中,当L为复平面上逐段光滑封闭曲线时,在L所围的内部和外部,Cauchy型积分解析;通过对Cauchy主值积分的讨论,可得Cauchy型积分在L上的左、右边值,且边值满足Plemelj公式.基于Koch曲线的构造方法,对一系列Cauchy型积分取极限,并附加上一定的Hlder条件,可得在Koch曲线所围的内部和外部区域内都解析的Cauchy型积分函数,进一步得到与经典解析函数边值问题类似的结果. |
| 关 键 词： | Koch曲线 解析函数 边界值 |
A Class of Boundary Value Problem for Analytic Functions Bounded by the Koch Curve |
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| RUAN Zheng-shun,LUO Ai-hua,WANG Xiao-lin.A Class of Boundary Value Problem for Analytic Functions Bounded by the Koch Curve[J].Mathematics in Practice and Theory,2011,41(12). | |
| Authors: | RUAN Zheng-shun LUO Ai-hua WANG Xiao-lin |
| Abstract: | In this paper,based on the formation of Koch Curve,through discussing the Umit function of a sequence of Cauchy-type integrals,a analytic Cauchy-type integral function was obtained in the interior region and exterior region bounded by Koch Curve attaching some Hldercondition.Furthermore,some similar results was got with the classical boundary value problems for analytic functions. |
| Keywords: | Koch Curve analytic function boundary value |
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