Mathematical Sciences: Interpolation by Meromorphic Matrix Functions

数学科学：亚纯矩阵函数插值

• 批准号: 9302590
• 负责人: Edward Azoff
• 金额: $ 7.88万
• 依托单位: University of Georgia Research Foundation Inc
• 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: 1993-08-15 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302590&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Interpolation; Meromorphic; Matrix

Work to be done on this project combines the mathematical theories of closed multiple-valued, matrix valued functions. The underlying motivation for the studies lies in the expected significant applications to systems theory and functional analysis. The research can be viewed from the point of view of interpolation theory and meromorphic matrix functions, or as explicit work on the correspondence between the Weil divisor approach and the factor of automorphy approach to complex vector bundles over closed Riemann surfaces. In the former one wants to construct meromorphic matrix valued functions interpolating given points on a closed Riemann surface. In the latter, one takes local solutions to form a holomorphic vector bundle and asks for conditions which guarantee that the bundle be trivial. This is where Weil's work enters. The work described in this project arises in systems analysis where one is interested in selecting optimal functions from classes all of whose members satisfy the same conditions. The conditions may be given as prescribed pointwise values of the functions. It then becomes essential that one first solve the interpolation problem to classify all such functions before establishing the optimal ones.

在此项目上要做的工作结合了封闭的多价值矩阵有价值函数的数学理论。 研究的基本动机在于系统理论和功能分析的预期重要应用。可以从插值理论和Meromorormormorgic矩阵函数的角度观察研究，或者是Weil除数方法之间的对应关系的明确工作，以及对封闭的Riemann表面上复杂矢量捆绑的自动形方法的因素。 在前者中，人们希望在封闭的riemann表面上构造给定点插值的函数。 在后者中，人们采用局部解决方案形成一个全态矢量束，并要求保证捆绑捆绑的条件是微不足道的。这是Weil的工作进入的地方。 该项目中描述的工作是在系统分析中产生的，其中人们有兴趣从所有成员满足相同条件的类中选择最佳功能。 条件可以作为函数的处方端值的规定值。 然后，必须首先解决插值问题以在建立最佳功能之前对所有此类功能进行分类。