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

Angela Pasquale[1]; Maddala Sundari[2]

  • [1] Université Paul Verlaine Laboratoire de Mathématiques et Applications (LMAM, UMR CNRS 7122) Bâtiment A, Ile du Saulcy 57045 Metz cedex 1 (France)
  • [2] Chennai Mathematical Institute Plot No. H1, SIPCOT IT Park Padur P.O. Siruseri 603 103 (India)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 859-886
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Pasquale, Angela, and Sundari, Maddala. "Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type." Annales de l’institut Fourier 62.3 (2012): 859-886. <http://eudml.org/doc/251126>.

@article{Pasquale2012,
abstract = {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 $t_0&gt;0$ 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.},
affiliation = {Université Paul Verlaine Laboratoire de Mathématiques et Applications (LMAM, UMR CNRS 7122) Bâtiment A, Ile du Saulcy 57045 Metz cedex 1 (France); Chennai Mathematical Institute Plot No. H1, SIPCOT IT Park Padur P.O. Siruseri 603 103 (India)},
author = {Pasquale, Angela, Sundari, Maddala},
journal = {Annales de l’institut Fourier},
keywords = {Uncertainty principle; Schrödinger equation; Helgason-Fourier transform; Beurling theorem; Hardy theorem; Beurling type rapid decreasing; Riemannian symmetric space},
language = {eng},
number = {3},
pages = {859-886},
publisher = {Association des Annales de l’institut Fourier},
title = {Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type},
url = {http://eudml.org/doc/251126},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Pasquale, Angela
AU - Sundari, Maddala
TI - Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 859
EP - 886
AB - 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 $t_0&gt;0$ 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.
LA - eng
KW - Uncertainty principle; Schrödinger equation; Helgason-Fourier transform; Beurling theorem; Hardy theorem; Beurling type rapid decreasing; Riemannian symmetric space
UR - http://eudml.org/doc/251126
ER -

References

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