Mathematical Sciences: Nonlinear Harmonic Analysis

数学科学：非线性调和分析

• 批准号: 8804281
• 负责人: Stephen Semmes
• 金额: --
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8804281&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Harmonic; Analysis

This project is for mathematical research on singular integral operators and related matters. These operators transform functions which may be quite chaotic in their behavior into functions which are very smooth. The study of their continuity properties, that is, how small changes in the input function show up in the transformed function, is basic to much of mathematical analysis. Such investigations are part of the research which Professor Semmes will undertake. Surfaces in space give rise to singular integral operators; these will be studied with the aim of relating continuity properties of the operators to geometric properties of the surfaces. A collateral group of problems to be pursued has to with the complex method of interpolation of Banach spaces from the viewpoint of differential geometry and differential equations.

这个项目是关于奇异的数学研究 积分算子及相关问题。 这些运营商 变换函数的行为可能非常混乱 转换成平滑的函数。 他们的研究 连续性属性，即输入中的微小变化 函数在变换后的函数中显示出来，是许多 数学分析 这些调查是 塞姆斯教授将要进行的研究 空间中的曲面引起奇异积分算子; 这些将被研究，目的是将连续性 操作符的几何属性 表面。 要解决的一组附带问题必须 使用Banach空间的复杂插值方法， 微分几何与微分观点 方程