Mathematical Sciences: Connections of Modern Analysis with Geometry and Topology

数学科学：现代分析与几何和拓扑的联系

• 批准号: 9003335
• 负责人: Ronald Douglas
• 金额: $ 19.55万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003335&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Connections; Modern; Analysis

Professor Douglas plans to continue his research in two areas: multivariable spectral theory and the study of invariants for differential operators on manifolds with boundary and on foliated manifolds. His research in multivariable operator theory will involve the study of Hilbert modules from the viewpoint of analytic and algebraic geometry. The study of invariants for differential operators will involve the Chern character for operators on a manifold with boundary. This research involves the theory of Hilbert space operators. These are essentially infinite matrices of complex numbers. Such objects have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important classes of Hilbert space operators.

道格拉斯教授计划在两个领域继续他的研究：多变量谱理论和带边界流形和带叶流形上的微分算子不变量的研究。他在多变量算子论方面的研究将涉及从解析几何和代数几何的观点研究希尔伯特模。微分算子不变量的研究将涉及到带边界流形上算子的陈氏性质。本研究涉及到希尔伯特空间算子的理论。它们本质上是复数的无限矩阵。这样的对象在应用科学的各个领域都有应用，在纯数学中也是如此。这类研究是对某些重要的Hilbert空间算子分类的一种尝试。