Mathematical Sciences: Problems in Operator Theory and Related Areas

数学科学：算子理论及相关领域的问题

• 批准号: 9101372
• 负责人: Hari Bercovici
• 金额: $ 6.68万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101372&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Operator; Theory

Professor Bercovici will study the properties of free additive and multiplicative convolution of measures in the convex plane, as well as applications of these operations to the calculation of spectral invariants. He will continue the study of spectral versions of the Nevanlinna-Pick, Caratheodory, and Nehari problems and explore their relations with control theory. Another topic of study will be the structure of dual algebras with an emphasis on algebras generated by a finite number of commuting operators. Professor Bercovici's research concerns operators on Hilbert space. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. Research of this type is an attempt to classify certain important families of such operators.

贝尔科维奇教授将研究自由添加剂的性质 和凸平面上测度的乘法卷积，如 以及这些运算在计算 谱不变量 他将继续研究光谱 Nevanlinna-Pick、Caratheodory和Nehari问题的版本 并探讨它们与控制理论的关系。 另一个话题 研究将是对偶代数的结构，重点是 由有限个交换算子生成的代数。 Bercovici教授的研究涉及希尔伯特算子 空间 Hilbert空间算子本质上是无限矩阵 复杂的数字。 这些运营商在每个 应用科学领域以及纯数学领域。 研究 这种类型的一种尝试是将某些重要的家庭分类 这样的运营商。