The Fourier transform on 2-step Lie groups

Guillaume Lévy (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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].

Domaines: Analyse classique [math.CA]

Guillaume Lévy. The Fourier transform on 2-step Lie groups. 2017. ⟨hal-01672322⟩