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

Angela Pasquale, Maddala 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.

Une version microlocale de la condition ( w ) de Verdier

David J. A. Trotman (1989)

Annales de l'institut Fourier

Kashiwara et Schapira ont proposé une condition de régularité appelée ( μ ) sur un couple de sous-variétés X , Y d’une variété C 2 M : ( T Y * M + ^ T X * M ) ∩ ( T * M ) | Y ⊆ T Y * M , où + ^ est une somme géométrique naturelle dans l’analyse microlocale. Nous démontrons que la ( μ )-régularité est équivalente à la ( w ) -régularité de Verdier, répondant ainsi à une question de Kashiwara.

Uniform controllability for the beam equation with vanishing structural damping

Ioan Florin Bugariu (2014)

Czechoslovak Mathematical Journal

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 ε ∈ ( 0 , 1 ) . We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls v ε as ε goes to zero. It is shown that for any time T sufficiently large but independent of ε and for each initial data in a suitable space there exists a uniformly bounded...

Unitons and their moduli.

Anand, Christopher Kumar (1996)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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