miyachi’s theorem
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2016 ◽  
Vol 229 ◽  
pp. 1-20 ◽  
Author(s):  
ALI BAKLOUTI ◽  
SUNDARAM THANGAVELU

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.


2013 ◽  
Vol 94 (1-2) ◽  
pp. 3-19
Author(s):  
F. Abdelmoula ◽  
A. Baklouti ◽  
D. Lahyani

2011 ◽  
Vol 22 (3) ◽  
pp. 167-173 ◽  
Author(s):  
F. Chouchene ◽  
R. Daher ◽  
T. Kawazoe ◽  
H. Mejjaoli

2010 ◽  
Vol 88 (1) ◽  
pp. 1-17 ◽  
Author(s):  
ALI BAKLOUTI ◽  
SUNDARAM THANGAVELU

AbstractWe formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.


2009 ◽  
Vol 61 (2) ◽  
pp. 551-558 ◽  
Author(s):  
Radouan DAHER ◽  
Takeshi KAWAZOE ◽  
Hatem MEJJAOLI
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