Mathematical Sciences: Complex Analysis

数学科学：复分析

• 批准号: 9102013
• 负责人: David Barrett
• 金额: $ 4.38万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 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: 1991-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102013&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Analysis

The principal investigator will study several problems in the geometry of domains in complex Euclidean space. In particular, he will investigate regularity properties of the Bergman projection operator which relates boundary behavior of holomorphic functions to their behavior on the interior of a domain. Another topic to be considered on this research project is the topology of Levi flat hypersurfaces. Both of these subjects require an analysis of the d"-operator on domains in n-dimensional complex space. This research continues the study of the geometry and analysis of functions of several complex variables. The theory of functions of one complex variable plays a central role in all branches of mathematics and physics. This research project will undertake continued research on functions of more than one variable which is analogous to the well studied classical situation. One surprising application of the research thus far has been to queuing theory which studies the order in which processes are performed.

首席研究员将研究复杂欧几里得空间中域几何的几个问题。特别是，他将研究伯格曼投影算子的正则性质，该算子将全纯函数的边界行为与其在域内部的行为联系起来。该研究项目要考虑的另一个主题是 Levi 平面超曲面的拓扑。这两门学科都需要对 n 维复空间域上的 d" 算子进行分析。这项研究继续研究几何和多个复变函数的分析。一个复变函数的理论起着核心作用。该研究项目将继续研究多个变量的函数，这类似于迄今为止经过深入研究的经典情况，即研究顺序的排队论。其中执行过程。