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HARDY AND MIYACHI THEOREMS FOR HEISENBERG MOTION GROUPS

  • ALI BAKLOUTI (a1) and SUNDARAM THANGAVELU (a2)

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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HARDY AND MIYACHI THEOREMS FOR HEISENBERG MOTION GROUPS

  • ALI BAKLOUTI (a1) and SUNDARAM THANGAVELU (a2)

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