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（项目C） 首席研究员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理论。他还计划研究单位圆盘上伯格曼空间的不变子空间的结构以及一般有界区域上伯格曼空间之间的乘子。 算子理论是现代数学的核心学科，研究矩阵的无限维推广。此类研究试图对满足根据关联运算符或底层空间给出的附加条件的运算符进行分类。 它们在每门应用科学以及纯数学中都有丰富的应用。举一个具体的例子，基本的H-无穷大控制问题之一是由Nevanlinna-Pick插值的经典数学理论发展而来的。该理论的应用包括汽车悬架系统的改进、飞机飞行控制、化学过程控制等。