Abstract
Abstract We investigate the negative part of the spectrum of the operator $$-\partial ^2 - \mu $$ - ∂ 2 - μ on $$L^2(\mathbb {R})$$ L 2 ( R ) , where a locally finite Radon measure $$\mu \ge 0$$ μ ≥ 0 serves as a potential. We obtain estimates for the eigenvalue counting function, for individual eigenvalues and estimates of the Lieb–Thirring type. A crucial tool for our estimates is Otelbaev’s function, a certain average of the measure-potential $$\mu $$ μ , which is used both in the proofs and the formulation of most of the results.