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. ***//

在该项目中，主要研究者将研究复杂分析和潜在理论中的许多问题。 特别是，他将研究全球性库奇问题解决方案的全球行为，各种潜在理论积分运算符的光谱，伯格曼空间上移动运算符的循环性以及在较高维度中的谐波功能的反射。 用于攻击如此多样性问题的技术是从部分微分方程，复杂分析和潜在理论的理论中得出的。 从历史上看，数学领域被称为偏微分方程的理论和复杂变量的理论相互紧密相关。 实际上，十九世纪的数学大部分时间围绕了部分微分方程与复杂变量之间的这种关系，每个区域都对彼此产生了深远的影响。 在这个项目中，主要研究人员将使用两个领域之间的这种共生关系来研究许多有趣的问题，这些问题涉及几个空间维度的谐波功能。 *** //