Lieb-Thirring inequalities on the half-line with critical exponent

Abstract

We consider the operator -d2/dr2 - V in L 2(ℝ+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound /(Equation Presented) for any α ∈ [0, 1) and γ ≥ (1 - α)/2. This includes a Lieb-Thirring inequality in the critical endpoint case. © European Mathematical Society 2008.