Mathematical Sciences: Multivariable Operator Theory

数学科学：多变量算子理论

• 批准号: 9623142
• 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: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-05-15 至 1999-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623142&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multivariable; Operator; Theory

9623142 SALINAS Professor Norberto Salinas proposes to investigate systems of operators and certain types of operator algebras, such as Toeplitz C*-algebras over pseudoconvex domains with transverse symmetries, using techniques from non-commutative differential geometry and from the theory of functions of several complex variables. He also plans to use techniques from algebraic topology (more specifically from K-theory) and from non-commutative harmonic analysis. The ultimate goal of the project is a deep understanding of the joint behavior of n-tuples of operators on Hilbert space. The focus of the research will be on the spectral and c*- algebraic properties of such n-tuples. The field of multivariable operator theory has become very active in the last ten years. It is central to many mathematical applications to physics, chemistry, biology, economics, computer sciences, business, and engineering. While Professor Norberto Salinas does not plan to develop these applications, the potential for these developments are apparent from the type of technology developed in his project.

9623142 SALINAS教授Norberto Salinas提出研究系统的运营商和某些类型的运营商代数，如Toeplitz C*-代数的pseudoconvular域与横向对称，使用技术从非交换微分几何和理论的功能，几个复变量。他还计划使用代数拓扑（更具体地说，从K理论）和非交换谐波分析的技术。该项目的最终目标是深入理解希尔伯特空间上的n元组算子的联合行为。研究的重点将是这样的n元组的频谱和c*-代数性质。在过去的十年中，多变量算子理论领域变得非常活跃。它是物理学、化学、生物学、经济学、计算机科学、商业和工程学中许多数学应用的核心。虽然Norberto Salinas教授不打算开发这些应用程序，但从他的项目中开发的技术类型来看，这些开发的潜力是显而易见的。