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

9502983乐透这个项目涉及全纯函数空间和这些空间上的算子的工作。该方案中的特殊问题包括de Brange-Rovnyak空间的乘子和插值序列的分类，Toeplitz和Hankel算子乘积的有界性(可能是无界的)，向后移位到算子值域的非循环向量之间的关系，Hardy空间中刚性函数的分类和这类函数在复合算子下的行为，度量分解在复合算子研究中的应用，三个或更多可交换对角化压缩算子的von Neumann不等式的研究，交换算子到可交换对角化算子的扰动，以及解析乘法算子压缩到后向移位算子的不变子空间的循环性。Hilbert空间算子是矩阵的无限推广。向量的无限推广经常是一个函数，因此，Hilbert空间算子经常被建模为函数空间上的乘法算子。这个项目涉及对作用于希尔伯特空间的一个变形的de Brange-Rovnyak空间上的算子的乘法模型的许多基本问题的研究。将所有这些问题联系在一起的主题是算子理论、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和更深入的理解，这比人们通过单独研究它们所希望的*

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 ***