Mathematical Sciences: Composition Operators on Analytic Spaces

数学科学：解析空间上的组合算子

• 批准号: 9300525
• 负责人: Barbara MacCluer
• 金额: $ 7.01万
• 依托单位: University of Richmond
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9300525&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Composition; Operators; Analytic

MacCluer will continue her research on several problems which lie at the interface of operator theory and function theory, involving composition operators on analytic function spaces. Identification of the spectrum of a composition operator acting on a Hilbert space of analytic functions on the unit ball in C^n will be of particular concern. Ross will study the invariant subspaces of Bergman spaces on certain slit domains and investigate the relationship between the geometry of the slit and the behavior of the functions near the slit. Operator theory is that part of mathematics that studies the infinite dimensional generalizations of matrices. In particular, when restricted to finite dimensional subspaces, an operator has the usual linear properties, and thus can be represented by a matrix. The central problem in operator theory is to classify operators satisfying additional conditions given in terms of associated operators (e.g. the adjoint) or in terms of the underlying space. Operator theory underlies much of mathematics, and many of the applications of mathematics to other sciences.

麦克卢尔将继续她对几个问题的研究 它位于算子理论和函数的交界处 理论，涉及解析函数上的复合算子 空间. 复合算子谱的识别 作用在单位球上解析函数的Hilbert空间上 在C^n中，将特别关注。 罗斯将研究 某些slit域上Bergman空间的不变子空间， 研究狭缝的几何形状与 狭缝附近函数的行为。 算子理论是数学中研究 矩阵的无穷维推广 特别是， 当限制到有限维子空间时，算子具有 通常的线性性质，因此可以表示为 矩阵 算子理论的中心问题是分类 满足附加条件的算子 关联算子（例如伴随算子）或 底层空间 算子理论是数学的基础， 以及数学在其他科学中的应用。