Mathematical Sciences: C*-Algebras, Operator Theory and Applications

数学科学：C*-代数、算子理论和应用

• 批准号: 9301187
• 负责人: Norberto Salinas
• 金额: --
• 依托单位: University of Kansas Main Campus
• 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: 1993-05-15 至 1996-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301187&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebras; Operator; Theory

Salinas will continue his research on Toeplitz C*-algebras over domains with non-abelian symmetries, spectral and C*- algebraic properties of Toeplitz operators on pseudoconvex domains, and weighted Wiener-Hopf operators on convex cones. Upmeier will continue his study of quantization theories in several complex variables with the main focus on new geometric situations. He will also study new types of special functions arising in quantization theory, and deepen the connections with microlocal analysis. 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.

萨利纳斯将继续他的研究Toeplitz C*-代数域与非阿贝尔对称性，频谱和C*-代数性质的Toeplitz运营商的pseudoclave域，并加权维纳-霍普夫运营商凸锥。Upmeier将继续他的量子化理论的研究在几个复杂的变量，主要集中在新的几何情况。他还将研究量子化理论中出现的新型特殊函数，并加深与微观局部分析的联系。算子论是数学中研究矩阵无限维推广的部分。特别是，当限制在有限维子空间时，算子具有通常的线性性质，因此可以用矩阵表示。算子理论的中心问题是对满足附加条件的算子进行分类，这些附加条件是根据相关算子（例如伴随算子）或根据底层空间给出的。算子理论是许多数学的基础，也是数学在其他科学中的许多应用的基础。