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Schrödinger equation on noncompact symmetric spaces

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03187413
Contributor : Hong-Wei Zhang <>
Submitted on : Thursday, April 1, 2021 - 7:58:10 AM
Last modification on : Thursday, April 8, 2021 - 3:26:08 AM

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Jean-Philippe Anker, Stefano Meda, Vittoria Pierfelice, Maria Vallarino, Hong-Wei Zhang. Schrödinger equation on noncompact symmetric spaces. 2021. ⟨hal-03187413⟩

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