Representation Theory and Harmonic Analysis on Homogeneous Spaces

齐次空间的表示论与调和分析

• 批准号: 1101337
• 负责人: Gestur Olafsson
• 金额: $ 21万
• 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: 2011
• 资助国家: 美国
• 起止时间: 2011-11-01 至 2015-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101337&HistoricalAwards=false
• 关键词: Representation; Theory; Harmonic; Analysis; Homogeneous

The proposed research covers a broad spectrum of problems and ideas reaching from abstract harmonic analysis on symmetric spaces, geometry, and infinite dimensional analogues, to classical questions in abelian harmonic analysis. The basic subject of the proposed research is harmonic analysis on symmetric spaces G/H which connects analysis, group theory (symmetry) and geometry. The project includes holomorphic extension of H-spherical distributions, applications of intertwining operators and evaluations of their spectrum, analysis on infinite dimensional spaces, representation theory and G-invariant Banach spaces of functions. The physical parts include reflection positivity and transfer operators. This work combines methods and ideas from several areas of mathematics: complex analysis, group actions on complex manifolds, classical harmonic analysis, applied mathematics, and quantum field theory.Harmonic analysis and representation theory are two central subjects of mathematics and play an important role in pure and applied mathematics as well as theoretical physics. Well known examples of applications are tomography and signal analysis, but the proposed research deals with more abstract and fundamental questions. The proposal is related to several parts of mathematics, both pure and applied, and includes several connections to physics, in particular quantum field theory in form of reflection positivity, and applied sciences. The research involves wide spectrum of collaboration including graduate students and a network of other researchers in the USA, Mexico, and Europe.

拟议的研究涵盖了各种各样的问题和思想，从对对称空间，几何和无限维度类似物的抽象谐波分析到Abelian谐波分析中的经典问题。拟议的研究的基本主题是对对称空间G/H的谐波分析，它连接分析，群体理论（对称）和几何形状。该项目包括H-Spherical分布的全态扩展，相互交织的操作员的应用以及对其频谱的评估，对无限维空间的分析，表示理论和G不变的BANACH功能空间。物理部件包括反射阳性和转移操作员。这项工作结合了数学几个领域的方法和思想：复杂的分析，复杂流形的小组动作，经典的谐波分析，应用数学以及量子＆＃64257; eld Theopery.Harmonic分析和表示理论是数学的两个核心主题，并且在纯和应用数学中起着重要作用。应用众所周知的示例是断层扫描和信号分析，但拟议的研究涉及更多抽象和基本问题。该提案与纯和应用的数学的几个部分有关，包括与物理学的几个联系，特别是反射阳性的形式和应用科学的量子场理论。该研究涉及广泛的合作，包括研究生以及美国，墨西哥和欧洲其他研究人员的网络。