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Some uncertainty principles for diamond Lie groups

  • Ali Baklouti EMAIL logo und Dhoha Lahyani
Veröffentlicht/Copyright: 25. Juni 2015
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Abstract

So far, the uncertainty principles for solvable non-exponential Lie groups have been treated only in few cases. The first author and Kaniuth produced an analogue of Hardy's theorem for a diamond Lie group, which is a semi-direct product of ℝd with the Heisenberg group 2d+1 In this setting, we formulate and prove in this paper some other uncertainty principles (Miyachi, Cowling–Price and Lp-Lq Morgan). This allows us to provide a refined version of Hardy's theorem and to study the sharpness problems.

MSC: 22E27; 32G05

Funding source: D.G.R.S.R.T

Award Identifier / Grant number: LR 11ES52

The authors are deeply indebted to the referee for having suggested us many valuable comments to get the present form of the paper.

Received: 2014-12-12
Revised: 2015-2-14
Accepted: 2015-2-20
Published Online: 2015-6-25
Published in Print: 2015-10-1

© 2015 by De Gruyter

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