Mathematical Sciences: Subnormal Operators and Banach Spaces of Holomorphic Functions

数学科学：次正规算子和全纯函数的 Banach 空间

• 批准号: 9531917
• 负责人: Liming Yang
• 金额: $ 3.81万
• 依托单位: University of Hawaii
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9531917&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Subnormal; Operators; Banach

Abstract of the project (item C) The principal investigator will continue to study the internal structure theory of subnormal operators, with particular consideration of finite rank self-commutator, the structure of invariant subspaces, and connections and applications to other fields. He will use operator theoretical tools to study the theory of quadrature domains. He also plans to investigate the structure of invariant subspaces of the Bergman space on the unit disk and multipliers between the Bergman spaces over a general bounded region. Operator theory is a central discipline in modern mathematics that studies infinite dimensional generalization of matrices. This type of research is an attempt to classify operators satisfying additional conditions given in terms of the associated operator or the underlying space. They have rich applications in every applied science as well as pure mathematics. To mention a specific example, one of basic H-infinity control problems was developed by the classical mathematical theory of Nevanlinna-Pick interpolation. Applications of the theory include improvement in automobile suspension systems, airplane flight control, chemical process control, etc.

项目摘要（C项） 主要研究者将继续研究次正规算子的内部结构理论，特别考虑有限秩自交换子，不变子空间的结构，以及与其他领域的联系和应用。他将使用算子理论工具来研究正交域的理论。他还计划调查的结构不变的子空间的伯格曼空间的单位磁盘和乘数之间的伯格曼空间在一般有界区域。 算子论是现代数学的一门中心学科，研究矩阵的无穷维推广。这种类型的研究是试图对满足附加条件的算子进行分类，这些附加条件是根据相关算子或 底层空间 它们在每一个应用科学中都有丰富的应用 以及纯数学。举一个具体的例子， 基本的H ∞控制问题是由经典的 Nevanlinna-Pick插值的数学原理的应用 理论包括汽车悬架系统的改进， 飞机飞行控制、化工过程控制等。