Mathematical Sciences: Composition Operators on Analytic Spaces

MacCluer将继续研究算子理论与函数理论的交叉领域，包括解析函数空间上的复合算子。在C^n的单位球上的解析函数的希尔伯特空间上的复合算子的谱的识别将是特别值得关注的。Ross将研究某些狭缝域上Bergman空间的不变子空间，并研究狭缝的几何形状与狭缝附近函数的行为之间的关系。算符理论是研究矩阵的无限维推广的数学部分。特别地，当限制在有限维子空间中时，算子具有通常的线性性质，因此可以用矩阵表示。算子理论的中心问题是对满足附加条件的算子进行分类，这些附加条件是根据相关算子（如伴随算子）或根据基础空间给出的。算子理论是许多数学的基础，也是数学在其他科学中的许多应用的基础。

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.