Théorie des groupes/Équations aux dérivées partielles
Équation des ondes sur les espaces symétriques riemanniens
[Wave equation on Riemannian symmetric spaces]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 725-728.

We prove that the solutions of the homogeneous wave equation on Riemannian symmetric spaces have dispersion properties and we deduce Strichartz type estimates for these solutions.

Nous montrons que les solutions de l'équation des ondes homogène sur des espaces symétriques riemanniens possèdent des propriétés de dispersion et nous déduisons des estimations de type Strichartz pour ces solutions.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.04.031
Hassani, Ali 1

1 Laboratoire Modal'X, UFR SEGMI, bâtiment G, Université Paris Ouest Nanterre-La Défense, 200, avenue de la République, 92001 Nanterre cedex, France
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Hassani, Ali. Équation des ondes sur les espaces symétriques riemanniens. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 725-728. doi : 10.1016/j.crma.2009.04.031. http://www.numdam.org/articles/10.1016/j.crma.2009.04.031/

[1] Anker, J.-Ph. The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi and Varadarajin, J. Funct. Anal., Volume 96 (1991) no. 2, pp. 331-349

[2] Bahouri, H.; Gerard, P.; Xu, C.-J. Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg, J. Anal. Math., Volume 82 (2000), pp. 93-118

[3] M. Beals, Time decay of Lp norms for solutions of wave equation on exterior domains, in: F. Colombini, N. Lerner (Eds.), Geometrical Optics and Related Topics, Progress in Nonlinear Differential Equations and Their Applications, vol. 32, pp. 59–77

[4] Ginibre, G.; Velo, G. Generalized Strichartz inequalities for the wave equation, J. Funct. Anal., Volume 133 (1995), pp. 50-86

[5] Lohoué, N. Lp estimates of solutions of wave equations on Riemannian manifolds, Lie groups and applications, Montreal, PQ, 1996 (CMS Conf. Proc.), Volume vol. 21, AMS, Providence, RI (1997), pp. 103-126

[6] Pierfelice, V. Weighted Strichartz estimates for the Schrödinger and wave equations on Damek–Ricci spaces, Math. Z., Volume 260 (2008) no. 2, pp. 377-392

[7] Skrzypczak, L. Besov spaces on symmetric manifolds. The atomic decomposition, Studia Math., Volume 124 (1997) no. 3, pp. 215-238

[8] Tataru, D. Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation, Trans. Amer. Math. Soc., Volume 353 (2001) no. 2, pp. 795-807

[9] Varadarajan, V.S. The method of stationary phase and applications to geometry and analysis on Lie groups, Algebraic and Analytic Methods in Representation Theory (Sonderborg, 1994), Perspect. Math., vol. 17, Academic Press, San Diego, CA, 1997, pp. 167-242

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