Mathematical Sciences: RUI: Spaces of Holomorphic Functions and Their Operators

数学科学：RUI：全纯函数空间及其运算符

• 批准号: 9502983
• 负责人: Benjamin Lotto
• 金额: $ 5万
• 依托单位: Vassar College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9502983&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Spaces; Holomorphic

9502983 Lotto This project involves work on spaces of holomorphic functions and operators on these spaces.. Particular problems in the proposal include the classification of the multipliers and interpolating sequences for de Branges-Rovnyak spaces, the boundedness of products of (possibly unbounded) Toeplitz and Hankel operators, the relationship of the noncyclic vectors of the backward shift to operator ranges, the classification of rigid functions in Hardy spaces and the behavior of such functions under composition, the use of disintegration of measures in the study of composition operators, the study of von Neumann's inequality for three or more commuting diagonalizable contractions, the perturbation of commuting operators to commuting diagonalizable operators and the cyclicity of the compression of analytic multiplication operators to an invariant subspace of the backward shift operator. Hilbert space operators are infinite generalizations of matrices. The infinite generalization of a vector is frequently a function and for this reason Hilbert space operators are frequently modeled as the operator of multiplication on a space of functions. This project involves the study of many basic problems of multiplication models for operators acting on a variant of Hilbert spaces called de Branges-Rovnyak spaces. The theme that connects all these problems is the interplay among operator theory, functional analysis, and complex function theory. The interplay provides a richer and deeper understanding of all three of these topics than one could hope for by studying them individually ***

小行星9502983 这个项目涉及工作空间的全纯函数和运营商在这些空间。特别的问题包括de Branges-Rovnyak空间的乘子和插值序列的分类，（可能是无界的）Toeplitz和Hankel算子，后移的非循环向量与算子值域的关系，哈代空间中刚性函数的分类以及这种函数在复合下的行为，在复合算子的研究中使用测度的分解，研究三个或更多可交换的可对角化压缩的冯·诺依曼不等式，交换算子到交换可对角化算子的扰动以及解析乘法算子压缩到后移不变子空间的循环性操作符. 希尔伯特空间算子是矩阵的无限推广。向量的无限推广通常是一个函数，因此希尔伯特空间算子经常被建模为函数空间上的乘法算子。这个项目涉及到许多基本问题的研究乘法模型的运营商作用于一个变种的希尔伯特空间称为德布朗日-Rovnyak空间。连接所有这些问题的主题是算子理论、泛函分析和复变函数理论之间的相互作用。相互作用提供了一个更丰富和更深入的了解所有这三个主题比一个人可以希望通过研究他们个别 *