Mathematical Sciences: Function Theory on Convex Domains

数学科学：凸域函数论

• 批准号: 8701038
• 负责人: Harold Boas
• 金额: $ 2.66万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-15 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701038&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Function; Theory; Convex

The project is concerned with mathematical research on the function theory on domains in the space of several complex variables. Fundamental ideas from complex analysis, partial differential equations, operator theory and integral representations are combined in these investigations. One basic goal - well understood in one variable but open in several variables - is the classification of domains into equivalence classes under holomorphic coordinate changes. Considerable progress has been made recently in this area through research on related problems of extending holomorphic maps to the boundary of regions. This was done by analysis of the Bergman projection operator. This focused attention on projections of functions onto holomorphic function spaces such as the Bergman and the Szego projections. Work will be done analyzing the regularity properties of these and related projections on convex domains. Corvex domains with real analytic boundary are of finite type so that well known methods of partial differential equations can be used to show that these projection operators preserve differentiability of functions in Sobolev spaces. Work will be done in expanding present methods and developing new tools to handle domains of infinite type.

该项目涉及的数学研究的 多复形空间中区域上的函数论 变量 从复杂的分析，局部的基本思想 微分方程、算子理论和积分 在这些调查中结合了陈述。 一个基本 目标-在一个变量中很好理解，但在几个变量中开放 变量-是将域分类为等价 全纯坐标变换下的类。 相当大 最近，通过对以下问题的研究， 全纯映射延拓到边界的相关问题 地区 这是通过分析伯格曼投影完成的 操作符. 这将注意力集中在将功能投射到 Bergman和Szego等全纯函数空间 预测。 我们将分析 这些性质和相关的凸域上的投影。 具有真实的解析边界的Corvex域是有限的 类型，因此众所周知的偏微分方法 方程可以用来表明，这些投影算子 Sobolev空间中函数的可微性。 工作 将在扩展现有方法和开发新的 处理无限类型域的工具。