Mathematical Sciences: Matrix Analysis and Toeplitz and Composition Operators

考恩将研究有界线性算子的结构 在哈代希尔伯特空间，伯格曼希尔伯特空间， 单位圆盘上解析函数的相关空间， 关于具体表示算子的逼近问题 来洞察更普遍的问题。 他将致力于 Bergman上复合算子的统一结果， 空间上的复合算子理论 强调空间之间相似性的分析函数， 最小化对特定空间的特殊特征的依赖。 算子理论是数学中研究 矩阵的无穷维推广 特别是， 当限制到有限维子空间时，算子具有 通常的线性性质，因此可以表示为 矩阵 算子理论的中心问题是分类 满足附加条件的算子 关联算子（例如伴随算子）或 底层空间 算子理论是数学的基础， 以及数学在其他科学中的应用。

Cowen will study the structure of bounded linear operators on the Hardy Hilbert space, the Bergman Hilbert space, and related spaces of analytic functions on the unit disk, approaching problems on concretely presented operators in order to gain insight into more general problems. He will work on unifying results concerning composition operators on Bergman and Hardy spaces into a theory of composition operators on spaces of analytic functions emphasizing similarities between spaces and minimizing reliance on special features of particular spaces. 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.