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Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type

Angela PasqualeMaddala Sundari — 2012

Annales de l’institut Fourier

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 t 0 > 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.

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