Mathematical Sciences: Analysis in Spaces of Analytic and Harmonic Functions

阿克斯勒和夏皮罗将继续研究经典函数论和算子理论之间的联系。特别令人感兴趣的是解析映射的函数论性质与相应的复合、Toeplitz和Hankel算子的算子论性质之间的关联。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。算子理论的核心问题是根据伴随算子(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。

Axler and Shapiro will continue their study of the connection between classical function theory and operator theory. Of particular interest will be the association between function theoretic properties of an analytic mapping and operator theoretic properties of the corresponding composition, Toeplitz, and Hankel operators. 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 problems 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.