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

Angela Pasquale (1) , Maddala Sundari (2)

1 LMAM - Laboratoire de Mathématiques et Applications de Metz
2 Chennai Mathematical Institute [Inde]

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.

Mots clés: Uncertainty principle; Schrödinger equation; Helgason-Fourier transform; Beurling theorem; Hardy theorem

Domaines: Mathématiques [math]

Angela Pasquale, Maddala Sundari. Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type. Annales de l'Institut Fourier, 2012, 62 (3), pp.859-886. ⟨10.5802/aif.2710⟩. ⟨hal-01279413⟩