Geometric Non-linear Harmonic Analysis

几何非线性谐波分析

• 批准号: 9701307
• 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: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9701307&HistoricalAwards=false
• 关键词: Geometric; Non; linear; Harmonic; Analysis

ABSTRACT-DMS 9701307 Semmes This project is largely concerned with notions of "complexity", i.e., concrete measurements of how complicated a given object is. Finite and combinatorial notions of complexity play a basic role in computer science, but one can also see analogous ideas at play in traditional areas of mathematics, in connection with analysis, geometry, and topology, for instance. In the present project we take much of our inspiration from the ideas and methods of real-variable harmonic analysis, but the structures that we consider will be predominantly geometric in nature. In asking what is "complexity" one should also ask what is "simplicity". Traditional mathematics offers a rich variety of answers to both questions, and these answers are often connected to various forms of computational efficiency. In this proposal we shall mostly be concerned with notions of geometric or combinatorial structure in which there are some nontrivial rules or patterns but perhaps also moderate amounts of bending, breaking, or other disturbances. In particular, we would like to develop new methods for identifying, measuring, and comparing forms of structure in ways that are flexible enough to accommodate substantial distortion.

摘要-DMS 9701307 塞姆斯 这个项目主要涉及“复杂性”的概念，即，一个给定物体复杂程度的具体度量。 复杂性的有限和组合概念在计算机科学中起着基础作用，但人们也可以在传统的数学领域中看到类似的想法，例如与分析，几何和拓扑学有关。 在本项目中，我们从实变量调和分析的思想和方法中获得了很多灵感，但我们考虑的结构将主要是几何性质的。 在问什么是“复杂性”的同时，我们也应该问什么是“简单性”。 传统数学为这两个问题提供了丰富多样的答案，这些答案通常与各种形式的计算效率有关。 在这个提议中，我们将主要关注几何或组合结构的概念，其中有一些非平凡的规则或模式，但也许也有适度的弯曲、断裂或其他干扰。 特别是，我们希望开发新的方法来识别，测量和比较结构形式的方式是足够灵活，以适应大量的扭曲。