Mathematical Research Letters

Volume 19 (2012)

Number 2

Control For Schrödinger operators on tori

Pages: 309 – 324

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n2.a4

Authors

Nicolas Burq (Université Paris Sud, Mathématiques, Bât 425, Orsay 91405, France)

Maciej Zworski (Mathematics Department, University of California at Berkeley, CA 94720, U.S.A.)

Abstract

A well-known result of Jaffard states that anarbitrary region on a torus controls, in the $ L^2 $sense, solutions of the free stationaryand dynamical Schrödinger equations.In this paper, we show that the same result is validin the presence of a potential, that is forSchrödinger operators, $ - \Delta + V $, $ V \in \CI $.

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