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Some uncertainty principles for diamond Lie groups

Authors
  • Baklouti, Ali
  • Lahyani, Dhoha
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Jun 25, 2015
Volume
6
Issue
4
Pages
199–213
Identifiers
DOI: 10.1515/apam-2015-5009
Source
De Gruyter
Keywords
License
Yellow

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 ℍ 2d+1 ${\mathbb {H}_{2d+1}}$ 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.

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