Mathematical Sciences: Principal Currents

数学科学：主电流

• 批准号: 9003069
• 负责人: Joel Pincus
• 金额: $ 9.8万
• 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: 1990-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003069&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Principal; Currents

Professor Pincus will continue his investigation of currents associated with the index structure of certain algebras of operators. In particular he will study certain bundles and sheaves which are associated to the local index which he invented as well as finer invariants. He will also study the geometric meaning of the principal function, an extension of the index which is also defined on the essential spectrum. Professor Pincus' research is in the general area of the theory of operators on Hilbert space. These operators are essentially infinite matrices of complex numbers. Such operators or linear transformations 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 categories of such objects.

平卡斯教授将继续他对洋流的研究 与某些代数的索引结构相关联， 运营商 特别是他将研究某些束， 与他发明的局部索引相关联的层 以及更精细的不变量。 他还将学习几何 主函数的意义，指数的扩展 其也在基本光谱上定义。 平卡斯教授的研究是在一般领域的 Hilbert空间上的算子理论这些运算符 复数的无限矩阵 等 运算符或线性变换在每个领域都有应用 应用科学领域以及纯数学领域。 这 一种类型的研究是试图将某些重要的 这类物体的种类。