Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type
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چکیده
— Let X be a Riemannian symmetric space of the noncompact type. We prove that the solution of the time-dependent Schrödinger equation on X with square integrable initial condition f is identically zero at all times t whenever f and the solution at a time t0 > 0 are simultaneously very rapidly decreasing. The stated condition of rapid decrease is of Beurling type. Conditions respectively of Gelfand-Shilov, Cowling-Price and Hardy type are deduced. Résumé. — Soit X un espace riemannien symétrique de type non-compact. On montre que la solution de l’équation de Schrödinger dépendante du temps sur X, avec condition initiale de carré intégrable f , est nulle en tout temps t lorsque f et la solution à un temps t0 > 0 donné sont simultanément très rapidement décroissantes. La condition de décroissance rapide considérée est de type Beurling. Des conditions respectivement de types Gelfand-Shilov, Cowling-Price et Hardy en sont déduites.
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