Mathematical Sciences: Complex Analysis

首席研究员将研究复欧几里得空间域几何中的几个问题。特别是，他将研究Bergman投影算子的正则性，它将全纯函数的边界行为与它们在域内的行为联系起来。本研究项目中要考虑的另一个主题是Levi平面超曲面的拓扑结构。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分析几个复杂变量的函数。单复变函数理论在数学和物理的各个分支中都起着中心作用。这个研究项目将继续研究多个变量的函数，这类似于研究得很好的经典情况。到目前为止，这项研究的一个令人惊讶的应用是排队论，它研究的是过程执行的顺序。

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.