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.

该项目涉及数学问题，这些问题是从算术几何的平均不平等现象中得出的，这些不平等与数学的各个部分有许多联系。 一个人可以将两个数字的算术和几何平均值视为有序对，然后迭代该配对。 这样一来，一个人总是达到相等数量的限制。 该原理将在功能分析的背景下进行研究，在功能分析的背景下，迭代的对象是不合规的线性运算符，而该过程而不是计算均值，是锥体内部内部映射的更一般的映射。 目的是找到独特的固定射线（特征向量）。 预计将在人口生物学中提出的问题提出应用。 在奇异扰动的背景下，其他持续的工作将在延迟微分方程上完成。 这里的目的是确定是否可以预测非恒定周期性解决方案 - 尤其是第四节，这是边界层现象研究中发生的问题。