Journal of the European Mathematical Society

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Volume 10, Issue 3, 2008, pp. 739–755
DOI: 10.4171/JEMS/128

Published online: 2008-09-30

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

Tomas Ekholm[1] and Rupert L. Frank[2]

(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