Hardy-Lieb-Thirring inequalities for fractional Schroedinger operators

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dc.creatorFrank, Rupert L.
dc.creatorLieb, Elliott H.
dc.creatorSeiringer, Robert
dc.date2006-10-19
dc.date2006-10-27
dc.date.accessioned2026-07-07T09:58:32Z
dc.date.available2026-07-07T09:58:32Z
dc.descriptionWe show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schroedinger-like operators remain true, with possibly different constants, when the critical Hardy-weight $C|x|^{-2}$ is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and, in particular, for relativistic Schroedinger operators. We also allow for the inclusion of magnetic vector potentials. As an application, we extend, for the first time, the proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge $Zα=2/π$.
dc.descriptionLaTeX2e, 29 pages; corrected version of Lemma 3.3
dc.identifierhttps://arxiv.org/abs/math/0610593
dc.identifierhttp://arxiv.org/abs/math/0610593
dc.identifierJ. Amer. Math. Soc. 21, 925-950 (2008)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167749
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.titleHardy-Lieb-Thirring inequalities for fractional Schroedinger operators
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