Mathematical Sciences: Holomorphic Spaces

数学科学：全纯空间

• 批准号: 9301508
• 负责人: John McCarthy
• 金额: $ 6.16万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301508&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Holomorphic; Spaces

McCarthy will study various spaces of holomorphic functions and the natural operators acting on these spaces. He will investigate the existence of radial or non-tangential boundary values for every function in an infinite dimensional Hilbert or Banach holomorphic space, and the connection between this phenomenon and the geometry of the space. He will also investigate how elements of holomorphic spaces can be decomposed into products of special functions, analogous to the inner-outer factoring in the classical Hardy spaces. 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.

麦卡锡将研究各种空间的全纯函数 以及作用在这些空间上的自然算子。 他将 研究是否存在径向或非切向边界 无穷维希尔伯特空间中的每个函数的值，或 Banach全纯空间，以及这两者之间的联系 现象和空间的几何形状。 他还将 研究全纯空间的元素如何分解 转化为特殊函数的乘积，类似于内外 经典哈代空间的因式分解。 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。