Application of methods of harmonic analysis

谐波分析方法的应用

• 批准号: 0070692
• 负责人: Charles Fefferman
• 金额: $ 58.6万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070692&HistoricalAwards=false
• 关键词: Application; methods; harmonic; analysis

Abstract Fefferman and Stein will study problems in harmonic analysis, including the decay of multilinear-operator-valued oscillatory integrals, the domination of pseudodifferential operators, ergodic theory on semisimple Lie groups, multi-parameter harmonic analysis and its applications to several complex variables, constructive methods in fluid mechanics, discrete versions of singular Radon transforms, scaling laws for mechanical systems, and applications of harmonic analysis to atoms. Harmonic analysis began with the work of Fourier in the early 19th century. Its theme is to analyze complex behavior (heat flow, vibration,...) by writing it as a sum of basic pieces behaving in the simplest way. Harmonic analysis is crucial in many parts of science and technology. Fefferman and Stein are pursuing ideas in harmonic analysis and relating them to problems in mathematics and physics.

Fefferman和Stein将研究调和分析中的问题，包括多线性算子值振荡积分的衰减、伪微分算子的支配、半单李群的遍历理论、多参数调和分析及其在几个复杂变量中的应用、流体力学中的构造方法、奇异Radon变换的离散版本、力学系统的标度定律以及调和分析在原子中的应用。谐波分析始于19世纪初傅立叶的工作。它的主题是分析复杂的行为（热流，振动，…），将其写成以最简单的方式表现的基本部分的总和。谐波分析在科学技术的许多领域都是至关重要的。费费曼和斯坦正在研究谐波分析的思想，并将其与数学和物理问题联系起来。