Mathematical Sciences: Multivariable Spectral Theory and Complex Analysis

数学科学：多变量谱理论和复分析

• 批准号: 9201729
• 负责人: Mihai Putinar
• 金额: $ 4.94万
• 依托单位: University of California-Riverside
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201729&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multivariable; Spectral; Theory

Putinar will investigate two sets of problems. The first concerns Toeplitz operators on multivariable Bergman spaces and their relevance for the function theory of several complex variables. He will relate the spectral problems for this class of operators to the theory of functions in pseudoconvex domains with L2-growth control at the boundary. The second set of problems is related to the theory of moments in Euclidean n- space. Putinar will try to determine methods for solving certain moment problems on semialgebraic subsets by using specific operator theories. 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.

普京将调查两组问题。 第一 涉及多变量Bergman空间上的Toeplitz算子， 它们与几个复变函数理论的相关性 变量 他将讲述这门课的光谱问题 从算子到伪凸域上的函数论 在边界处具有L2生长控制。 第二组 问题是有关的时刻在欧几里德n理论- 空间 普京将试图确定解决某些问题的方法， 半代数子集上的矩问题 运营商理论 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。