The Fourier transform on 2-step Lie groups
Classical Analysis and ODEs
2017-12-29 v1
Abstract
In this paper, we investigate the behavior of the Fourier transform on finite dimensional 2-step Lie groups and develop a general theory akin to that of the whole space or the torus. We provide a familiar framework in which computations are made sensibly easier than with the usual representation-theoretic Fourier transform. In addition, we study the 'singular frequencies' of the group, at which the canonical bilinear antisymmetric form degenerates. We also exhibit a specific example for which partial degeneracy of the canonical form occurs, as opposed to the full degeneracy at the origin. We thus extend the results from [1].
Cite
@article{arxiv.1712.09880,
title = {The Fourier transform on 2-step Lie groups},
author = {Guillaume Lévy},
journal= {arXiv preprint arXiv:1712.09880},
year = {2017}
}