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Uncertainty inequalities for the Heisenberg group
Xiao Jin-Sen 1, He Jian-Xun 2 *
1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006
2. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006
*Correspondence author
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Funding: NSF（No.10971039）, RFDP（No.200810780002）
Opened online:12 January 2012
Accepted by: none
Citation: Xiao Jin-Sen , He Jian-Xun.Uncertainty inequalities for the Heisenberg group[OL]. [12 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4459786
 
 
In this article, we extend the Heisenberg-Pauli-Weyl uncertainty inequality on the Euclidean space to the Heisenberg group. We use the estimate of the heat kernel together with the relation between thesublaplacian and the group Fourier transform to develop the uncertainty inequality on the Heisenberg group. By this inequality we obtain the Heisenberg-Pauli-Weyl uncertainty inequality for the continuous wavelet transform.
Keywords:Heisenberg group; Fourier transform;wavelet transform; uncertainty inequality; heat kernel
 
 
 

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