Lieb-Thirring estimates for singular measures

TL;DR

This paper establishes Lieb-Thirring estimates for the sum of powers of negative eigenvalues of Schrödinger operators with singular measures, extending spectral bounds to more general measure settings.

Contribution

It introduces Lieb-Thirring estimates for Schrödinger operators involving singular measures, broadening the scope of spectral analysis in mathematical physics.

Findings

Lieb-Thirring estimates are proved for operators with singular measures.

The estimates depend on measure conditions on balls in d.

Results extend classical bounds to singular measure contexts.

Abstract

Lieb-Thirring type estimates are proved for the sum of powers of negative eigenvalues of a Schr\"odinger type operator $(-\Delta)^l -V\mu$ where $\mu$ is a singular measure in $\mathbb{R}^d,$ satisfying a condition on the measure of balls and $V$ is a $\mu$-measurable function.