Harmonic Analysis on Lie Groups and Spectral Symmetry

李群与谱对称的调和分析[i: G. Olafsson， lsu]摘要该项目涉及现代分析和科学中有关几何、群作用形式的对称性以及李群与对称空间的调和分析之间相互作用的各种问题。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积极性。这个建议结合了数学的不同分支。这包括通过Hardy空间的复数分析，表示的解析延拓，和广义Bargmann-Segal变换；对称空间形式的几何、对偶性与紧化李群的积分变换与表示。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.