Mathematical Sciences: Harmonic Analysis Methods in OperatorTheory and Modern Analysis

数学科学：算子理论和现代分析中的调和分析方法

• 批准号: 9401009
• 负责人: Earl Berkson
• 金额: $ 7.5万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401009&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Harmonic; Analysis; Methods

9401009 Berkson The investigations seek to develop a broad abstract operator theory which expands the role of harmonic analysis in the structures of general analysis. In this program, the powerful methods of harmonic analysis will be harnessed to operator theory by expanding the theory and scope of transference methods. These investigations constitute a fertile ongoing program of fundamental research which has been successfully applied to numerous disciplines in recent years. The directions and themes will include the following mainstream topics: multiplier theory and transference of maximal estimates for Fourier multipliers; wavelet decompositions for Fourier multipliers; interpolation methods and transference; ergodic theory; abstract spectral decompositions. The planned research will seek a wide unified overview of mathematical applications. Historically such an approach is crucial to disciplines such as quantum physics, which rely for their explication on broad abstract principles of mathematics. ***

小行星9401009 这些调查旨在发展一个广泛的抽象算子理论，扩大调和分析在一般分析结构中的作用。 在这个程序中，强大的谐波分析方法将利用算子理论，扩大理论和范围的迁移方法。 这些调查构成了一个肥沃的基础研究，近年来已成功地应用于许多学科正在进行的计划。 方向和主题将包括以下主流主题：乘数理论和傅立叶乘数的最大估计的转移;傅立叶乘数的小波分解;插值方法和转移;遍历理论;抽象谱分解。 计划中的研究将寻求数学应用的广泛统一概述。 从历史上看，这种方法对量子物理等学科至关重要，这些学科依赖于广泛的抽象数学原理。 ***