A lower bound on the first spectral gap of Schrödinger operators with Kato class measures
نویسنده
چکیده
We study Schrödinger operators on Rn formally given by Hμ = −∆− μ, where μ is a positive, compactly supported measure from the Kato class. Under the assumption that a certain condition on the μ-volume of balls is satisfied and that Hμ has at least two eigenvalues below the essential spectrum σess(Hμ) = [0,∞), we derive a lower bound on the first spectral gap of Hμ. The assumption on the μ-volume of balls is in particular satisfied if μ is of the form μ = aσM , where M is a compact (n−1)-dimensional Lipschitz submanifold of Rn, σM the surface measure on M , and 0 6 a ∈ L∞(M). MSC 2000: 35J10, 35P15, 47A55
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