Sharp Lieb-Thirring Inequalities in High Dimensions

Abstract

We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schrödinger operator leads to Lieb-Thirring inequalities with sharp constants $L_{\gamma ,d}^{cl}$ with $\gamma \ge 3/2$ and arbitrary $d\ge 1$. (revised, to appear in Acta Math)