Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type
Annales de l'Institut Fourier, Volume 62 (2012) no. 3, p. 859-886

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.

Soit X un espace riemannien symétrique de type non-compact. On montre que la solution de l’équation de Schrödinger dépendante du temps sur X, avec condition initiale de carré intégrable f, est nulle en tout temps t lorsque f et la solution à un temps t 0 >0 donné sont simultanément très rapidement décroissantes. La condition de décroissance rapide considérée est de type Beurling. Des conditions respectivement de types Gelfand-Shilov, Cowling-Price et Hardy en sont déduites.

Received : 2010-11-03
Accepted : 2011-02-11
DOI : https://doi.org/10.5802/aif.2710
Classification:  43A85,  58Jxx
Keywords: Uncertainty principle, Schrödinger equation, Helgason-Fourier transform, Beurling theorem, Hardy theorem
@article{AIF_2012__62_3_859_0,
     author = {Pasquale, Angela and Sundari, Maddala},
     title = {Uncertainty principles for the Schr\"odinger equation on Riemannian symmetric spaces of the noncompact type},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {3},
     year = {2012},
     pages = {859-886},
     doi = {10.5802/aif.2710},
     zbl = {1253.43007},
     mrnumber = {3013810},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2012__62_3_859_0}
}
Pasquale, Angela; Sundari, Maddala. Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type. Annales de l'Institut Fourier, Volume 62 (2012) no. 3, pp. 859-886. doi : 10.5802/aif.2710. aif.centre-mersenne.org/item/AIF_2012__62_3_859_0/

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