Geometric configuration and Fourier analysis

几何配置和傅里叶分析

• 批准号: 0901553
• 负责人: Alex Iosevich
• 金额: $ 30.35万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901553&HistoricalAwards=false
• 关键词: Geometric; configuration; Fourier; analysis

The main thrust of this proposal is the study of k-point configurations in discrete, continuous and arithmetic settings. The basic question is to determine how large a subset of a given vector space needs to be to ensure that it determines a substantial proportion of all possible finite point configurations up to congruence. The research involves a tight interaction between analytic, number theoretic and combinatorial methods in a seamless symbiosis that allows for a deeper understanding of the associated techniques and ideas. The techniques and ideas of the proposal do not only involve interaction between different areas of mathematics. They also involve ideas from theoretical computer science with potential applications to data mining, coding, signal processing, bioinformatics and many other areas of modern science. Modern harmonic analysis, which is PI?s main area of expertise, is a treasure trove of techniques and ideas that have found relevance in virtually every scientific disciplines and this influence will continue to grow in the years and decades to come.

该建议的主旨是研究离散、连续和算术设置中的k点构型。基本问题是确定给定向量空间的子集需要多大，以确保它确定所有可能的有限点配置的相当大的比例，直到同余。该研究涉及分析，数论和组合方法之间的紧密互动，无缝共生，从而更深入地了解相关技术和思想。该提案的技术和思想不仅涉及不同数学领域之间的相互作用。它们还涉及理论计算机科学的思想，这些思想可能应用于数据挖掘，编码，信号处理，生物信息学和现代科学的许多其他领域。现代谐波分析，哪个是π？的主要专业领域，是一个技术和思想的宝库，几乎在每一个科学学科都发现了相关性，这种影响将在未来几年和几十年继续增长。