Negative Eigenvalue Estimates for the 1D Schrödinger Operator with Measure-Potential

Journal article, 2026

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