| 泛Clifford分析中无界域上的Cauchy积分公式和Cauchy-Pompeiu公式 |
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| 引用本文： | 许娜,杜金元.泛Clifford分析中无界域上的Cauchy积分公式和Cauchy-Pompeiu公式[J].数学杂志,2010,30(4). |
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| 作者姓名： | 许娜 杜金元 |
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| 作者单位： | 1. 河北科技大学经济管理学院,河北,石家庄,050018;武汉大学数学与统计学院,湖北,武汉,430072
2. 武汉大学数学与统计学院,湖北,武汉,430072 |
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| 基金项目： | Supported by NNSF of China(10471107); Doctor Start-up Fund Research of Hebei University of Science and Technology(QD200942) |
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| 摘 要： | 本文研究了泛Clifford分析中的Cauchy积分公式和Cauchy-Pompeiu公式.通过引入修正的Cauchy核,得出了取值在泛Clifford代数上的两公式在无界域上的表达式.此两公式是有界域上的相应结果的推广,并为研究无界域上的边值问题打下了基础.
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| 关 键 词： | 泛Clifford分析 Cauchy积分公式 Cauchy-Pompeiu公式 无界域 |
CAUCHY INTEGRAL FORMULA AND CAUCHY-POMPEIU FORMULA ON UNBOUNDED DOMAINS IN UNIVERSAL CLIFFORD ANALYSIS |
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| XU Na,DU Jin-yuan.CAUCHY INTEGRAL FORMULA AND CAUCHY-POMPEIU FORMULA ON UNBOUNDED DOMAINS IN UNIVERSAL CLIFFORD ANALYSIS[J].Journal of Mathematics,2010,30(4). |
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| Authors: | XU Na DU Jin-yuan |
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| Institution: | XU Na~(1,2),DU Jin-yuan~2 (1.School of Economics & Management,Hebei University of Science and Technology,Shijiazhuang 050018,China) (2.School of Math.and Statistics,Wuhan University,Wuhan 430072,China) |
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| Abstract: | In this article, we study the Cauchy integral formula and Cauchy-Pompeiu formula in universal Clifford analysis. By introducing the modified Cauchy kernel, we obtain the two formulas for functions with values in a universal Clifford algebra on unbounded domains. They are the extension of the results on bounded domains and lay a strong foundation for studying the boundary value problem on unbounded domains. |
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| Keywords: | universal Clifford analysis Cauchy integral formula Cauchy-Pompeiu formula unbounded domains |
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