Mathematical Sciences: Composition Operators on Analytic Spaces

MacCluer将继续研究位于算子论和函数论交界处的几个问题，涉及解析函数空间上的复合算子。C^n中单位球上的解析函数的Hilbert空间上作用的复合算子的谱的识别将是一个特别重要的问题。Ross将研究某些狭缝区域上Bergman空间的不变子空间，并研究狭缝的几何和狭缝附近函数的行为之间的关系。算子论是研究矩阵的无限维广义的数学部分。特别地，当被限制在有限维子空间时，算子具有通常的线性性质，因此可以用矩阵来表示。算子理论中的中心问题是根据伴随算子(例如伴随算子)或基础空间对满足附加条件的算子进行分类。算符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。

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.