Totally Disconnected and Locally Compact Heisenberg-Weyl Groups |
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Authors: | A. Vourdas |
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Affiliation: | 1. Department of Computing, University of Bradford, Bradford, BD7 1DP, UK
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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[mathbbZp,mathbbZp,mathbbZp]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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