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.

该项目要做的工作结合了封闭多值矩阵值函数的数学理论。 这些研究的根本动机在于预期在系统理论和泛函分析中的重要应用。该研究可以从插值理论和亚纯矩阵函数的角度来看待，也可以作为Weil除数方法和闭黎曼曲面上复向量丛的自同构因子之间对应关系的明确工作。 在前一种情况下，我们想要构造亚纯矩阵值函数，对封闭黎曼曲面上的给定点进行插值。 在后者中，人们采用局部解来形成全纯向量丛，并要求保证该丛是平凡的条件。这就是韦尔工作的切入点。 该项目中描述的工作出现在系统分析中，人们感兴趣的是从所有成员都满足相同条件的类中选择最佳函数。 条件可以被给出为函数的规定的逐点值。 因此，在建立最佳函数之前，首先解决插值问题以对所有此类函数进行分类就变得至关重要。