Lower bounds for Schrödinger operators in H¹(ℝ)

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Département de Mathématiques, Université de Bretagne Occidentale, 6, Avenue le Georgeu, BP 809 29285 Brest, France

We prove trace inequalities of type

{| | u' | |}^{2}_{L^{2}} + \sum_{j \in ℤ} k_{j} {| u (a_{j}) |}^{2} \geq λ {| | u | |}^{2}_{L^{2}}

where

u \in H^{1} (ℝ)

, under suitable hypotheses on the sequences

{a_{j}}_{j \in ℤ}

and

{k_{j}}_{j \in ℤ}

, with the first sequence increasing and the second bounded.

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