Abstract
Harmonic analysis on ℤ(p ℓ) and the corresponding representation of the Heisenberg-Weyl group HW[ℤ(p ℓ),ℤ(p ℓ),ℤ(p ℓ)], is studied. It is shown that the HW[ℤ(p ℓ),ℤ(p ℓ),ℤ(p ℓ)] with a homomorphism between them, form an inverse system which has as inverse limit the profinite representation of the Heisenberg-Weyl group \(\mathfrak {HW}[{\mathbb{Z}}_{p},{\mathbb{Z}}_{p},{\mathbb{Z}}_{p}]\). Harmonic analysis on ℤ p is also studied. The corresponding representation of the Heisenberg-Weyl group HW[(ℚ p /ℤ p ),ℤ p ,(ℚ p /ℤ p )] is a totally disconnected and locally compact topological group.
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Communicated by Hans G. Feichtinger.
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Vourdas, A. Totally Disconnected and Locally Compact Heisenberg-Weyl Groups. J Fourier Anal Appl 16, 748–767 (2010). https://doi.org/10.1007/s00041-010-9125-6
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DOI: https://doi.org/10.1007/s00041-010-9125-6