Mathematical Sciences: Interactions Between Functional Analysis, Harmonic Analysis and Probability

数学科学：泛函分析、调和分析和概率之间的相互作用

• 批准号: 9424396
• 负责人: Stephen Montgomery-Smith
• 金额: $ 7.89万
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9424396&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Interactions; Between; Functional

9424396 Montgomery-Smith This project involves work on two different fronts. The first involves harmonic analysis on abelian groups whose dual is ordered. The project involves taking traditional results from harmonic analysis, specifically those concerning analyticity and the conjugate function, and generalizing them to a new setting. This project will be based on a synthesis of a classification theorem of Hahn on ordered groups together with modern techniques such as martingale theory, Browninan motion and the geometry of Banach spaces. The second project involves spectral properties of semigroups. This work has applications to the asymptotic behavior of differential equations in the case where the coefficients are infinite dimensional. Functional analysis seeks to understand the rigorous side of the kind of analysis that was needed to study functions that arise as solutions of differential equations. Harmonic analysis is concerned with studying the Fourier transform of functions. Probability, theory originally invented to understand events of chance, is now a technical subject related to measure theory. This project involves a blending of theses areas of mathematics. The results will be of use to a broad spectrum of mathematicians with the potential for application in systems theory.

小行星9424396 该项目涉及两个不同方面的工作。第一个涉及调和分析阿贝尔群的对偶是有序的。该项目涉及传统的结果，从谐波分析，特别是那些有关解析性和共轭函数，并将其推广到一个新的设置。这个项目将基于一个综合的分类定理哈恩有序群连同现代技术，如鞅论，布朗运动和几何的Banach空间。第二个项目涉及半群的谱性质。这项工作的微分方程的渐近行为的情况下，系数是无穷维的应用。 泛函分析试图理解研究作为微分方程解出现的函数所需的那种分析的严格方面。调和分析是研究函数的傅里叶变换。概率，最初是为了理解偶然事件而发明的理论，现在是一个与测量理论相关的技术学科。这个项目涉及数学的这些领域的融合。结果将是使用广泛的数学家在系统理论中的应用潜力。