Mathematics – Analysis of PDEs
Scientific paper
2010-11-04
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.
Pasquale Angela
Sundari Maddala
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