Mathematical Sciences: Complex Analysis

首席研究员将研究几个问题， 复欧氏空间中的域几何。他特别 将研究伯格曼投影的正则性 全纯函数边界性态的算子 它们在域内部的行为。另一个话题是 在这个研究项目中考虑的是Levi平坦的拓扑 超曲面这两个问题都需要分析 n维复空间中域上的d”-算子 本研究延续了几何学和分析的研究， 多个复变量的函数。理论的职能 一个复变函数在所有分支中起着核心作用。 数学和物理。该研究项目将承担 继续研究一个以上变量的函数， 类似于研究得很好的经典情况。一个令人惊讶 到目前为止，研究的应用是排队论 它研究过程执行的顺序。

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.