Mathematical Sciences: Analysis in Spaces of Analytic and Harmonic Functions

Axler和Shapiro将继续研究经典函数理论和算子理论之间的联系。特别感兴趣的将是解析映射的函数理论性质与相应组合、Toeplitz和Hankel算子的算子理论性质之间的联系。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，这些附加条件是由关联算子（如伴随算子）或基础空间给出的。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。

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.