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将继续在Hankel运营商及其应用程序上工作。 特别是，他们将研究自动伴侣操作员的光谱特性及其与持续时间和离散时间的平衡实现的关系；完全常规的矢量固定随机过程的光谱表征； 基质值函数的超级近似值；以及有限等级的特殊近似Hankel运算符，重复初始运算符的第一个单数值。 操作者理论是研究矩阵无限尺寸概括的数学部分。 特别是，如果仅限于有限的尺寸子空间，则操作员具有通常的线性属性，因此可以用矩阵表示。 操作者理论中的核心问题是对操作员进行分类，以满足相关操作员（例如伴随）或基础空间方面给出的其他条件。 操作者理论是数学的大部分基础，以及数学对其他科学的应用。