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HARDY AND MIYACHI THEOREMS FOR HEISENBERG MOTION GROUPS

Part of: Lie groups

Published online by Cambridge University Press:  20 October 2016

ALI BAKLOUTI
Affiliation:
Department of Mathematics, Faculty of Sciences at Sfax, Route de Soukra, 3038, Sfax, Tunisia email Ali.Baklouti@fss.rnu.tn
SUNDARAM THANGAVELU
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India email veluma@math.iisc.ernet.in

Abstract

Let $G=\mathbb{H}^{n}\rtimes K$ be the Heisenberg motion group, where $K=U(n)$ acts on the Heisenberg group $\mathbb{H}^{n}=\mathbb{C}^{n}\times \mathbb{R}$ by automorphisms. We formulate and prove two analogues of Hardy’s theorem on $G$ . An analogue of Miyachi’s theorem for $G$ is also formulated and proved. This allows us to generalize and prove an analogue of the Cowling–Price uncertainty principle and prove the sharpness of the constant $1/4$ in all the settings.

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© 2016 by The Editorial Board of the Nagoya Mathematical Journal  

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HARDY AND MIYACHI THEOREMS FOR HEISENBERG MOTION GROUPS
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