2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58294We 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 $L^{cl}_{γ,d}$ with $γ\ge 3/2$ and arbitrary $d\ge 1$. (revised, to appear in Acta Math)Mathematical PhysicsSpectral Theory35P15; 35L15; 47A75; 35J10text