Control for Schrödinger Operators on 2-tori: Rough Potentials
نویسندگان
چکیده
For the Schrödinger equation, (i∂t + ∆)u = 0 on a torus, an arbitrary nonempty open set Ω provides control and observability of the solution: ‖u|t=0‖L2(T2) ≤ KT ‖u‖L2([0,T ]×Ω). We show that the same result remains true for (i∂t + ∆ − V )u = 0 where V ∈ L(T), and T is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for V ∈ C(T) and conjectured for V ∈ L∞(T2). The higher dimensional generalization remains open for V ∈ L∞(Tn).
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