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Let be a Riemannian symmetric space of the noncompact type. We prove that the solution of the time-dependent Schrödinger equation on with square integrable initial condition is identically zero at all times whenever and the solution at a time 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.
Kashiwara et Schapira ont proposé une condition de régularité appelée ( sur un couple de sous-variétés d’une variété , où est une somme géométrique naturelle dans l’analyse microlocale. Nous démontrons que la )-régularité est équivalente à la -régularité de Verdier, répondant ainsi à une question de Kashiwara.
This paper is devoted to studying the effects of a vanishing structural damping on the controllability properties of the one dimensional linear beam equation. The vanishing term depends on a small parameter . We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls as goes to zero. It is shown that for any time sufficiently large but independent of and for each initial data in a suitable space there exists a uniformly bounded...
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