no. 5
Nonlinear Schrödinger Equation on Real Hyperbolic Spaces
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1853-1869. 
@article{AIHPC_2009__26_5_1853_0,
     author = {Anker, Jean-Philippe and Pierfelice, Vittoria},
     title = {Nonlinear {Schr\"odinger} {Equation} on {Real} {Hyperbolic} {Spaces}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1853--1869},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.01.009},
     mrnumber = {2566713},
     zbl = {1176.35166},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.009/}
}
TY  - JOUR
AU  - Anker, Jean-Philippe
AU  - Pierfelice, Vittoria
TI  - Nonlinear Schrödinger Equation on Real Hyperbolic Spaces
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 1853
EP  - 1869
VL  - 26
IS  - 5
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.009/
DO  - 10.1016/j.anihpc.2009.01.009
LA  - en
ID  - AIHPC_2009__26_5_1853_0
ER  - 
%0 Journal Article
%A Anker, Jean-Philippe
%A Pierfelice, Vittoria
%T Nonlinear Schrödinger Equation on Real Hyperbolic Spaces
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 1853-1869
%V 26
%N 5
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.009/
%R 10.1016/j.anihpc.2009.01.009
%G en
%F AIHPC_2009__26_5_1853_0
Anker, Jean-Philippe; Pierfelice, Vittoria. Nonlinear Schrödinger Equation on Real Hyperbolic Spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1853-1869. doi : 10.1016/j.anihpc.2009.01.009. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.009/

[1] Anker J.-Ph., L p Fourier Multipliers on Riemannian Symmetric Spaces of the Noncompact Type, Ann. of Math. 132 (1990) 597-628. | MR | Zbl

[2] Anker J.-Ph., Damek E., Yacoub C., Spherical Analysis on Harmonic an Groups, Ann. Sc. Norm. Super. Pisa 33 (1996) 643-679. | Numdam | MR | Zbl

[3] Banica V., The Nonlinear Schrödinger Equation on the Hyperbolic Space, Comm. Partial Differential Equations 32 (10) (2007) 1643-1677, arXiv:math/0406058. | MR | Zbl

[4] Banica V., Carles R., Staffilani G., Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space, Geom. Funct. Anal. 18 (2) (2008) 367-399. | MR

[5] Bourgain J., Fourier Transformation Restriction Phenomena for Certain Lattice Subsets and Application to the Nonlinear Evolution Equations I - Schrödinger Equations, Geom. Funct. Anal. 3 (2) (1993) 107-156. | MR | Zbl

[6] Burq N., Gérard P., Tzvetkov N., Strichartz Inequalities and the Nonlinear Schrödinger Equation on Compact Manifolds, Amer. J. Math. 126 (3) (2004) 569-605. | MR | Zbl

[7] Cowling M. G., Herz's “principe De Majoratio” and the Kunze-Stein Phenomenon, in: Harmonic Analysis and Number Theory, Montreal, 1996, CMS Conf. Proc., vol. 21, Amer. Math. Soc., 1997, pp. 73-88. | MR | Zbl

[8] P. Gérard, V. Pierfelice, Nonlinear Schrödinger equation on four-dimensional compact manifolds, Bull. Soc. Math. Fr., in press.

[9] Ginibre J., Velo G., Generalized Strichartz Inequalities for the Wave Equation, J. Funct. Anal. 133 (1) (1995) 50-68. | MR | Zbl

[10] Helgason S., Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978, Amer. Math. Soc., 2001. | MR | Zbl

[11] Helgason S., Groups and Geometric Analysis (Integral Geometry, Invariant Differential Operators, and Spherical Functions), Academic Press, 1984, Amer. Math. Soc., 2002. | MR | Zbl

[12] Helgason S., Geometric Analysis on Symmetric Spaces, Amer. Math. Soc., 1994. | MR | Zbl

[13] Ionescu A. D., An Endpoint Estimate for the Kunze-Stein Phenomenon and Related Maximal Operators, Ann. of Math. (2) 152 (1) (2000) 259-275. | MR | Zbl

[14] A.D. Ionescu, G. Staffilani, Semilinear Schrödinger flows on hyperbolic spaces - scattering in H 1 , preprint, 2008.

[15] Kato T., On Nonlinear Schrödinger Equations, Ann. Inst. H. Poincaré (A) Phys. Theor. 46 (1) (1987) 113-129. | Numdam | MR | Zbl

[16] Keel M., Tao T., Endpoint Strichartz Estimates, Amer. J. Math. 120 (5) (1998) 955-980. | MR | Zbl

[17] Pierfelice V., Weighted Strichartz Estimates for the Radial Perturbed Schrödinger Equation on the Hyperbolic Space, Manuscripta Math. 120 (4) (2006) 377-389. | MR | Zbl

[18] Pierfelice V., Weighted Strichartz Estimates for the Schrödinger and Wave Equations on Damek-Ricci Spaces, Math. Z. 260 (2) (2008) 377-392. | MR | Zbl

[19] Tao T., Visan M., Zhang X., Global Well-Posedness and Scattering for the Defocusing Mass-Critical Nonlinear Schrödinger Equation for Radial Data in High Dimensions, Duke Math. J. 140 (1) (2007) 165-202. | MR

Cité par Sources :