Mathematical Sciences: Complex Analysis and Potential Theory

数学科学：复分析与势论

• 批准号: 9022938
• 负责人: Dmitry Khavinson
• 金额: $ 1.6万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9022938&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Analysis; Potential

In this project the principal investigator will study a number of problems in complex analysis and potential theory. In particular, he will investigate the global behavior of solutions of holomorphic Cauchy problems, the spectra of various potential theoretic integral operators, the cyclicity of the shift operator on Bergman spaces, and the reflection of harmonic functions in higher dimensions. The techniques used to attack such a diversity of problems are drawn from the theory of partial differential equations, complex analysis and potential theory. Historically the areas of mathematics known as the theory of partial differential equations and the theory of complex variables have been closely associated with each other. Indeed much of nineteenth century mathematics revolved around this relationship between partial differential equations and complex variables, with each area having a profound influence on the other. In this project the principal investigator will use this symbiotic relationship between the two areas to study a number of interesting problems involving harmonic functions in several space dimensions. ***//

在这个项目中，主要研究者将研究一个 复分析和位势理论中的一些问题。 在 特别是，他将研究解决方案的全球行为 全纯Cauchy问题的各种位势的谱 理论积分算子，移位算子的循环性 伯格曼空间上，以及调和函数在伯格曼空间中的反射 更高的维度 用来攻击这样一个 多样性的问题都是从偏理论中得出的 微分方程、复分析和位势理论。 历史上数学领域被称为理论 偏微分方程和复变理论 变量之间有着密切的联系。 确实 十九世纪的大部分数学都围绕着这一点 偏微分方程与复变函数的关系 变量，每一个领域都有深刻的影响， 其他. 在这个项目中，首席研究员将使用 两个方面的共生关系进行了一些研究， 有趣的问题涉及调和函数在几个 空间维度***//