Journal of the European Mathematical Society
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Published online: 2008-09-30
Lieb–Thirring inequalities on the half-line with critical exponentTomas Ekholm and Rupert L. Frank (1) Royal Institute of Technology, Stockholm, Sweden
(2) Caltech, Pasadena, United States
We consider a Schrödinger operator on the half-line with a Dirichlet boundary condition at the origin and show that moments of its negative eigenvalues can be estimated by the part of the potential that is larger than the critical Hardy weight. The estimate is valid for the critical value of the moment parameter.
Keywords: Schrödinger operator, Lieb–Thirring inequalities, Hardy inequality
Ekholm Tomas, Frank Rupert: Lieb–Thirring inequalities on the half-line with critical exponent. J. Eur. Math. Soc. 10 (2008), 739-755. doi: 10.4171/JEMS/128