Mathematical Sciences: Hankel Operators and Their Applications

特里尔和佩勒将继续他们对汉克尔的研究 运营商及其应用。 特别是，他们将 自伴Hankel算子谱性质研究 以及它们与平衡实现的关系， 时间和离散时间; 完全正则向量平稳随机过程; 矩阵值函数的超最优逼近;以及 有限秩重复Hankel算子的特殊逼近 初始算子的第一奇异值。 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。

Treil and Peller will continue their work on Hankel operators and their applications. In particular, they will investigate spectral properties of self-adjoint Hankel operators and their relations with balanced realizations with continuous time and with discrete time; spectral characterizations of the completely regular vectorial stationary random processes; superoptimal approximations of matrix-valued functions; and special approximation by finite rank Hankel operators that repeat first singular values of the initial operator. 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.