Mathematical Sciences: Linear Operators and Complex Variables

数学科学：线性运算符和复变量

• 批准号: 9500954
• 负责人: Mihai Putinar
• 金额: $ 6.5万
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500954&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Linear; Operators; Complex

9500954 Putinar This project involves continued research in multivariable spectral theory and in the theory of hyponormal operators. In the first area, standard cohomological methods will be combined with hard analysis techniques of several complex variables in the study of a class of Hilbert modules over function algebras. In the second area, a novel correspondence between quadrature domains and hyponormal operators will be exploited and expanded in both directions. The research will focus on several new and not yet fully investigated relations between two areas of mathematical analysis: function theory and operator theory. The benefits are expected to be on both sides, with a great potential of further research and with applications to computational mathematics and quantum physics. ***

9500954 Putinar这个项目包括继续研究多变量谱理论和次变态算子理论。在第一个领域，标准上同调方法将结合几个复杂变量的硬分析技术来研究一类函数代数上的希尔伯特模。在第二个领域，将在两个方向上开发和扩展正交域和次正规算子之间的一种新的对应关系。研究将集中在数学分析的两个领域：函数理论和算子理论之间的几个新的和尚未充分研究的关系。预计双方都将受益，具有进一步研究和应用于计算数学和量子物理的巨大潜力。* * *