Harmonic Analysis on Lie Groups and Spectral Symmetry

Louisiana State University, Baton Rouge LA

Investigators

Abstract

Proposal DMS 0070607 Harmonic Analysis on Lie Groups and Spectral Symmetry PI: G. Olafsson, LSU Abstract Tis 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 includes complex analysis 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.