Half-line Schrödinger Operators with No Bound States
نویسندگان
چکیده
We consider Schödinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if ∆+V has no spectrum outside of the interval [−2, 2], then it has purely absolutely continuous spectrum. In the continuum case we show that if both −∆+V and −∆−V have no spectrum outside [0,∞), then both operators are purely absolutely continuous. These results extend to operators with finitely many bound states.
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تاریخ انتشار 2003