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arXiv · 1712.09880

The Fourier transform on 2-step Lie groups

Guillaume Lévy
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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].

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Guillaume Lévy. 2017-12-28. The Fourier transform on 2-step Lie groups. https://arxiv.org/abs/1712.09880

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