Mathematical Analysis
Uncertainty principle and LpLq-sufficient pairs on noncompact real symmetric spaces
Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 889-892.

We consider a real semi-simple Lie group G with finite center and a maximal compact sub-group K of G. Let G=K exp (𝔞 + ¯)K be a Cartan decomposition of G. For xG denote ∥x∥ the norm of the 𝔞 + -component of x in the Cartan decomposition of G. Let a>0,b>0 and 1⩽p,q⩽∞. In this Note we give necessary and sufficient conditions on a,b such that for all K-bi-invariant measurable function f on G, if eax2fLp(G) and e bλ 2 (f)L q (𝔞 + * ) then f=0 almost everywhere.

On considère un groupe de Lie semi-simple réel G de centre fini et K un sous-groupe compact maximal de G. Soit G=K exp (𝔞 + ¯)K une décomposition de Cartan de G. Pour xG, on note ∥x∥ la norme de la composante de x dans 𝔞 + . Soient a>0,b>0 et 1⩽p,q⩽∞. Dans cette Note on donne une condition nécessaire et suffisante sur a,b telle que pour toute fonction f mesurable et K-bi-invariante sur G, si eax2fLp(G) et e bλ 2 (f)L q (𝔞 + * ) alors f=0 presque partout.

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Accepted:
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DOI: 10.1016/S1631-073X(03)00220-6
Ben Farah, Slaim 1; Mokni, Kamel 1

1 Faculté des sciences de Monastir, département de mathématiques, 5019 Monastir, Tunisia
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Ben Farah, Slaim; Mokni, Kamel. Uncertainty principle and LpLq-sufficient pairs on noncompact real symmetric spaces. Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 889-892. doi : 10.1016/S1631-073X(03)00220-6. http://www.numdam.org/articles/10.1016/S1631-073X(03)00220-6/

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