Harmonic Analysis on Lie Groups and Spectral Symmetry

李群和谱对称性的调和分析

• 批准号: 0070607
• 负责人: Gestur Olafsson
• 金额: $ 8.64万
• 依托单位: Louisiana State 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: 2000-08-01 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070607&HistoricalAwards=false
• 关键词: Harmonic; Analysis; Lie; Groups; Spectral

Proposal DMS 0070607Harmonic Analysis on Lie Groups and Spectral SymmetryPI: G. Olafsson, LSUAbstractTis project deals with a variety of problems in modern analysis and science relating the interplay between geometry, symmetries in the form of group actions, and harmonic analysis on Lie groups and symmetric spaces. The program is motivated in part by questions in mathematical physics and quantum field theory involving generalized causality and reflection positivity.The proposal combines different branches of mathematics. This includescomplexanalysis through Hardy spaces, analytic continuation of representations,and the generalized Bargmann-Segal transform; geometry in form of symmetric spaces, duality and compactification; integral transforms and representations of Lie groups. Several parts of the program are to be done collaboratively with colleagues in the USA and Europe.

提案DMS 0070607关于谎言组和光谱对称性的hMaronic分析：G。Olafsson，Lsuabstracttis项目在现代分析中处理了各种问题，并涉及与几何形式，群体行动形式的相互作用以及对群体和对称空间的和谐分析之间的相互作用，对称性的相互作用。该计划的一部分是由数学物理学和量子场理论中的问题进行的，涉及普遍的因果关系和反思阳性。该提案结合了数学的不同分支。这包括通过强烈的空间，表示的分析延续以及广义的Bargmann-Segal变换。以对称空间，二元性和压实形式形式的几何形状；谎言群体的整体变换和表示。 该计划的几个部分将与美国和欧洲的同事合作。