On the Uniqueness of Solutions of the Schrödinger Equation on Riemannian Symmetric Spaces of the Noncompact Type

Details On the Uniqueness of Solutions of the Schrödinger Equation on Riemannian Symmetric Spaces of the Noncompact Type On the Uniqueness of Solutions of the Schrödinger Equation on Riemannian Symmetric Spaces of the Noncompact Type

2010-11-04

arxiv.org/abs/1011.1066v3

Mathematics

Analysis of PDEs

20 pages, To appear in Annales de l Institut Fourier

Scientific paper

Let X be a Riemannian symmetric space of the noncompact type. We prove that the solution of the time-dependent Schr\"odinger 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.

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