Comptes Rendus
no. 13-14
Théorie des groupes/Équations aux dérivées partielles
Équation des ondes sur les espaces symétriques riemanniens
[Wave equation on Riemannian symmetric spaces]

Presented by: Jean-Michel Bony

Ali Hassani1
1 Laboratoire Modal'X, UFR SEGMI, bâtiment G, Université Paris Ouest Nanterre-La Défense, 200, avenue de la République, 92001 Nanterre cedex, France
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

Ali Hassani 1

1 Laboratoire Modal'X, UFR SEGMI, bâtiment G, Université Paris Ouest Nanterre-La Défense, 200, avenue de la République, 92001 Nanterre cedex, France 
@article{CRMATH_2009__347_13-14_725_0,
     author = {Ali Hassani},
     title = {\'Equation des ondes sur les espaces sym\'etriques riemanniens},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {725--728},
     publisher = {Elsevier},
     volume = {347},
     number = {13-14},
     year = {2009},
     doi = {10.1016/j.crma.2009.04.031},
     language = {fr},
}
TY  - JOUR
AU  - Ali Hassani
TI  - Équation des ondes sur les espaces symétriques riemanniens
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 725
EP  - 728
VL  - 347
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2009.04.031
LA  - fr
ID  - CRMATH_2009__347_13-14_725_0
ER  - 
%0 Journal Article
%A Ali Hassani
%T Équation des ondes sur les espaces symétriques riemanniens
%J Comptes Rendus. Mathématique
%D 2009
%P 725-728
%V 347
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2009.04.031
%G fr
%F CRMATH_2009__347_13-14_725_0
Ali Hassani. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.031/

[1] J.-Ph. Anker 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] H. Bahouri; P. Gerard; C.-J. Xu 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] G. Ginibre; G. Velo Generalized Strichartz inequalities for the wave equation, J. Funct. Anal., Volume 133 (1995), pp. 50-86

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

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

[8] D. Tataru 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] V.S. Varadarajan 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

Cited by Sources:

Comments - Policy