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

Tomas EkholmRupert Frank — 2008

Journal of the European Mathematical Society

We consider the operator - d 2 / d r 2 - V in L 2 ( + ) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound tr ( - d 2 / d r 2 - V ) - γ C γ , α + ( V ( r ) - 1 / ( 4 r 2 ) ) + γ + ( 1 + α ) / 2 r α d r for any α [ 0 , 1 ) and γ ( 1 - α ) / 2 . This includes a Lieb-Thirring inequality in the critical endpoint case.

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