| 摘要: |
| 本文主要讨论一类角度为θ=π/α,α≥1/2的扇形域上高阶多解析方程的Schwarz边值问题.通过构造适当的高阶-Schwarz算子和Pompeiu算子,我们给出了详细的解表达式.本文把边值问题进一步推广到高阶情形,丰富了扇形域上边值问题的发展. |
| 关键词: Schwarz问题 高阶-Schwarz算子 Pompeiu算子 |
| DOI： |
| 分类号:O174.5;O175.8 |
| 基金项目:Supported by Tianyuan Foundation of China (11326087);the Fundamental Research Funds for the Central Universities;the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry. |
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| HIGH ORDER SCHWARZ BOUNDARY VALUE PROBLEM IN A SECTOR |
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WANG Ying1, YE Liu-qing2, TONG Li-zhen1
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1.School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China;2.Dept. of Math., Jiaozuo Teachers College, Jiaozuo 454002, China
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| Abstract: |
| In this paper, we give a general discussion of Schwarz problem for polyanalytic equations in a sector with angle θ=π/α, α≥1/2. By constructing proper Poly-Schwarz and Pompeiu operators, the explicit solvability expressions for Schwarz problem are obtained, which extends the related result to higher order case and enriches the development of boundary problems in a sector. |
| Key words: Schwarz problem Poly-Schwarz operator Pompeiu operator |
