Schrödinger equation on noncompact symmetric spaces
Équation de Schrödinger sur les espaces symétriques non-compacts
Résumé
We establish sharp-in-time pointwise kernel estimates for the Schrödinger equation on noncompact symmetric spaces of general rank. A well-known difficulty in higher rank analysis, namely the fact that the Plancherel density is not a differential symbol in general, is overcome by using a spectral decomposition introduced recently by two of the authors in the study of the wave equation. We deduce the dispersive property of the Schrödinger propagator and prove global-in-time Strichartz inequalities for a large family of admissible pairs. As consequences, we extend the global well-posedness and small data scattering results previously obtained on real hyperbolic spaces to general Riemannian symmetric spaces of noncompact type.
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