Negative eigenvalue estimates for the 1D Schr{\"o}dinger operator with measure-potential

We investigate the negative part of the spectrum of the operator -∂² - μ on L²( R), where a locally finite Radon measure μ ≥ 0 is serving 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 μ, which is used both in the proofs and the formulation of most of the results.