Mathematical Sciences: Nonlinear Functional Analysis

数学科学：非线性泛函分析

• 批准号: 8803495
• 负责人: Roger Nussbaum
• 金额: $ 5万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-15 至 1990-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803495&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Functional; Analysis

This project concerns mathematical questions deriving from classical results on the arithmetic-geometric mean inequalities which have many connections with diverse parts of mathematics. One can view the arithmetic and geometric mean of two numbers as an ordered pair and then iterate this pairing. In doing so, one always arrives at a limit of equal numbers. This principle will be studied in the context of functional analysis in which the objects of the iteration are noncommuting linear operators and the process, instead of computing means, is a more general one of mappings of the interior of a cone into itself. The objective will be to find unique fixed rays (eigenvectors). Applications are expected to be made to questions arising in population biology. Other, continuing, work will be done on delay- differential equations in the context of a singular perturbations. The objectives here are to determine whether or not nonconstant periodic solutions can be predicted - especially of period four, a problem which occurs in the study of boundary layer phenomena.

这个项目涉及的数学问题， 算术-几何平均不等式的经典结果 它与数学的各个部分都有很多联系。 人们可以将两个数字的算术和几何平均值视为 一个有序的配对，然后重新排序这个配对。 在这样做时，一 总是达到相等数量的极限。 这项原则将 在功能分析的背景下进行研究， 迭代的对象是非交换线性算子， 该过程而不是计算装置是更一般的过程， 一个圆锥内部到自身的映射。 客观 将是找到唯一的固定射线（特征向量）。 应用 预计将对人口中出现的问题作出反应， 生物学 其他的，持续的，工作将被推迟- 奇异微分方程 扰动 这里的目标是确定是否或 不是非恒定的周期解可以预测-特别是 第四阶段，边界研究中出现的问题 层现象