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Lower bounds for Schrödinger operators in H¹(ℝ)

Ronan Pouliquen — 1999

Studia Mathematica

We prove trace inequalities of type $| | u^{'} {| |}_{L^{2}}^{2} + \sum_{j \in ℤ} k_{j} | u (a_{j}) |^{2} {\geq λ | | u | |}_{L^{2}}^{2}$ 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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