2017/12/28 by Guillaume Lévy, Lévy, Guillaume
Earth and Planetary Sciences · Mathematics · #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1712.09880
openalex publication_date 2017/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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].