2010/12/06 by Joseph A. Wolf, Wolf, Joseph A.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Theory of Mathematics #Relativity and Gravitational Theory #math.CA
paper · pdf · doi:10.48550/arxiv.1012.1289
Expository article; to appear in Edizioni della Scuola Normale di Pisa
arxiv created 2010/12/06 · openalex publication_date 2010/12/06 · arxiv updated 2010/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 those of the classical Fourier transform and Fourier inversion theories in one real variable.