Author:
BAKLOUTI ALI,THANGAVELU SUNDARAM
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.
Publisher
Cambridge University Press (CUP)
Cited by
3 articles.
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1. Uncertainty Principles for Heisenberg Motion Group;Abstract and Applied Analysis;2021-11-28
2. Hardy’s theorem for the continuous wavelet transform;Journal of Pseudo-Differential Operators and Applications;2019-11-25
3. Miyachi’s Theorem for the Quaternion Fourier Transform;Circuits, Systems, and Signal Processing;2019-08-31