Mathematical Sciences: Hankel Operators and Their Applications

数学科学：汉克尔算子及其应用

• 批准号: 9304011
• 负责人: Serguei Treil
• 金额: $ 11.6万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304011&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hankel; Operators; Their

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.

Treil 和 Peller 将继续他们在 Hankel 算子及其应用方面的工作。 特别是，他们将研究自伴 Hankel 算子的谱特性及其与连续时间和离散时间平衡实现的关系；完全正则向量平稳随机过程的谱特征； 矩阵值函数的超最优近似；以及重复初始算子的第一个奇异值的有限秩 Hankel 算子的特殊近似。 算子理论是研究矩阵无限维推广的数学部分。 特别是，当限制为有限维子空间时，算子具有通常的线性属性，因此可以用矩阵表示。 算子理论的中心问题是对满足根据关联算子（例如伴随）或基础空间给出的附加条件的算子进行分类。 算子理论是许多数学以及数学在其他科学中的许多应用的基础。