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Some uncertainty principles for diamond Lie groups

Some uncertainty principles for diamond Lie groups 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 ℝ d with the Heisenberg group ℍ 2 d + 1 ${\mathbb {H}_{2d+1}}$ In this setting, we formulate and prove in this paper some other uncertainty principles (Miyachi, Cowling–Price and L p - L q Morgan). This allows us to provide a refined version of Hardy's theorem and to study the sharpness problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

Some uncertainty principles for diamond Lie groups

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Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam-2015-5009
Publisher site
See Article on Publisher Site

Abstract

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 ℝ d with the Heisenberg group ℍ 2 d + 1 ${\mathbb {H}_{2d+1}}$ In this setting, we formulate and prove in this paper some other uncertainty principles (Miyachi, Cowling–Price and L p - L q Morgan). This allows us to provide a refined version of Hardy's theorem and to study the sharpness problems.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Oct 1, 2015

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