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

9502983 Lotto这个项目涉及全纯函数空间和这些空间上的算子的研究。具体问题包括de Branges-Rovnyak空间的乘子和插值序列的分类，Toeplitz算子和Hankel算子（可能无界）乘积的有界性，向算子值域倒移的非循环向量的关系，Hardy空间中刚体函数的分类及其复合下刚体函数的行为，测度分解在复合算子研究中的应用。研究了三个或更多可交换对角化缩的von Neumann不等式，交换算子对可交换对角化算子的摄动以及解析乘法算子压缩到倒移算子的不变子空间的循环性。希尔伯特空间算子是矩阵的无限推广。向量的无限泛化通常是一个函数，因此希尔伯特空间算子通常被建模为函数空间上的乘法算子。这个项目涉及研究许多基本问题的乘法模型的算子作用于希尔伯特空间的变体称为德布朗日-罗夫尼亚克空间。将所有这些问题联系起来的主题是算子理论、泛函分析和复函数理论之间的相互作用。这种相互作用提供了对这三个主题的更丰富、更深入的理解，而不是单独研究它们所能达到的效果

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 ***