Mathematical Sciences: RUI: Linear- Fractional Models and Their Applications

数学科学：RUI：线性-分数阶模型及其应用

• 批准号: 9401206
• 负责人: Paul Bourdon
• 金额: $ 6.45万
• 依托单位: Washington and Lee University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401206&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Linear; Fractional

9401206 Bourdon The project focuses on intertwining maps for holomorphic functions on the open disc. Given a holomorphic map a model can be constructed using the pair consisting of the intertwining map and the associated map. The project considers how change in the original map affect the intertwining component of the model. In particular, computer investigations will be made of the convergence properties of a sequence of intertwiners for a given holomorphic map. Progress in understanding these linear-fractional models will provide insight into both the behavior of composition operators and the dynamics of holomorphic self-maps under iteration. The project involves the interplay of operator theory and function theory. Operator theory is that part of mathematics that studies the infinite generalization of matrices. Classical function theory provides a source of models for operator theory. The current project involves a study of such function theoretic models. The importance of this work is a consequence of connections with iterative graphic computer computations. Undergraduate student involvement in the project will have a long term benefit for science. ***

小行星9401206 该项目的重点是开圆盘上全纯函数的交织映射。给定一个全纯映射，可以用交织映射和关联映射构成的映射对构造一个模型。该项目考虑了原始地图的变化如何影响模型的交织组件。特别是，计算机调查将作出的一个序列的交织为一个给定的全纯映射的收敛性质。在理解这些线性分数模型的进展将提供洞察复合算子的行为和迭代下的全纯自映射的动力学。 该项目涉及算子理论和函数理论的相互作用。算子理论是数学的一部分，研究矩阵的无限推广。经典函数论为算子论提供了模型来源。 目前的项目涉及对这种函数理论模型的研究。这项工作的重要性是与迭代图形计算机计算连接的结果。 本科生参与该项目将对科学产生长期的好处。 ***