Harmonic Analysis on Lie Groups and Spectral Symmetry

建议DMS 0070607关于李群和谱对称的调和分析PI：G.Olafsson，LSUAbstryTis项目处理现代分析和科学中的各种问题，涉及几何之间的相互作用，群作用形式的对称性，以及关于李群和对称空间的调和分析。该计划的部分动机是数学物理和量子场论中的问题，涉及广义因果关系和反射正性。该提议结合了不同的数学分支。这包括通过Hardy空间的复杂性分析、表示的解析延拓和广义Bargmann-西格尔变换；对称空间形式的几何、对偶和紧化；李群的积分变换和表示。该计划的几个部分将与美国和欧洲的同事合作完成。

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.