Mediterranean Journal of Mathematics

, Volume 10, Issue 1, pp 333–351 | Cite as

Uncertainty Inequalities on Laguerre Hypergroup

  • Rahmouni Atef


In this paper, we give analogues of local uncertainty inequality on \({\mathbb{R}^n}\) for stratified Laguerre hypergroup, connected with the spectral analysis of a given homogeneous sublaplacian L, also indicate how local uncertainty inequalities imply global uncertainty inequalities. It would be interesting to note that we deduce the local uncertainty inequalities for the radial functions on the Heisenberg group. Finally, we extend Heisenberg-Pauli-Weyl uncertainty inequality by ultracontractive properties of the semigroups generated by the differential operator and on the estimate on the heat kernel.

Mathematics Subject Classification (2010)

Primary 43A62 Secondary 42B10 


Heisenberg-Pauli-Weyl inequality local uncertainty principle heat kernel Laguerre hypergroup Laguerre Fourier transform 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesUniversity of CarthageBizerteTunisia

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