Classical analysis and nilpotent Lie groups

Abstract

Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I’ll describe how this goes for nilpotent Lie groups and for a class of Riemannian manifolds closely related to a nilpotent Lie group structure. There are also some infinite dimensional analogs but I won’t go into that here. The analytic ideas are not so different from the classical Fourier transform and Fourier inversion theories in one real variable.KeywordsUnitary RepresentationHeisenberg GroupHaar MeasureSpherical FunctionCompact Abelian GroupThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.