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On Lieb-Thirring Inequalities for Schrödinger Operators with Virtual Level


We consider the operator H=−Δ−V in L 2(ℝd), d≥3. For the moments of its negative eigenvalues we prove the estimate Similar estimates hold for the one-dimensional operator with a Dirichlet condition at the origin and for the two-dimensional Aharonov-Bohm operator.

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Correspondence to T. Ekholm.

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Communicated by B. Simon

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Ekholm, T., Frank, R. On Lieb-Thirring Inequalities for Schrödinger Operators with Virtual Level. Commun. Math. Phys. 264, 725–740 (2006).

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