Mathematical Sciences: Problems in Harmonic Analysis and Several Complex Variables

数学科学：调和分析和几个复变量问题

• 批准号: 9500758
• 负责人: Song-Ying Li
• 金额: $ 3.78万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500758&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Harmonic; Analysis

9500758 Li Li will investigate several problems in complex analysis, including the Corona problem in several complex variables; the theory of function spaces, such as Hardy spaces, Bergman spaces, and Lipschitz spaces, on domains in complex Euclidean space; and operator theory on function spaces. He will also study the boundary value problem of complex non-linear differential equations. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms.

9500758李丽将研究复数分析中的几个问题，包括若干复数变量中的电晕问题；复欧几里德空间上Hardy空间、Bergman空间、Lipschitz空间等函数空间的理论；以及函数空间上的算子理论。他还将研究复杂非线性微分方程的边值问题。本世纪初出现了几个复变量，作为一个复变量函数研究的自然产物。很明显，这个理论与它的前身有很大的不同。底层的几何结构更难掌握，而函数理论与一阶偏微分算子的关系要密切得多。因此，它成长为一门混合学科，结合了微分几何和微分方程的深层特征。许多基本结构是在过去三十年中确定的。目前的研究仍然集中在理解这些基本的数学形式。