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Lieb-Thirring inequalities on the half-line with critical exponent
Department of Mathematics, Lund University.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 10, no 3, 739-755 p.Article in journal (Refereed) Published
Abstract [en]

We consider the operator -d(2)/dr(2) - V in L-2(R+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound for any alpha is an element of [0, 1) and gamma >= (1 - alpha)/2. This includes a Lieb-Thirring inequality in the critical endpoint case.

Place, publisher, year, edition, pages
2008. Vol. 10, no 3, 739-755 p.
Keyword [en]
SCHRODINGER-OPERATORS
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-7027ISI: 000257869200006OAI: oai:DiVA.org:kth-7027DiVA: diva2:11904
Note
QC 20100708. Uppdaterad från Accepted till Published 20100708.Available from: 2007-04-25 Created: 2007-04-25 Last updated: 2012-01-27Bibliographically approved
In thesis
1. Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators
Open this publication in new window or tab >>Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis is devoted to quantitative questions about the discrete spectrum of Schrödinger-type operators.

In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬values remain true, with possibly different constants, when the critical Hardy weight is subtracted from the Laplace operator.

In Paper II we prove that the one-dimensional analog of this inequality holds even for the critical value of the moment parameter. In Paper III we establish Hardy-Lieb-Thirring inequalities for fractional powers of the Laplace operator and, in particular, relativistic Schrödinger operators. We do so by first establishing Hardy-Sobolev inequalities for such operators. We also allow for the inclu¬sion of magnetic fields.

As an application, in Paper IV we give a proof of stability of relativistic matter with magnetic fields up to the critical value of the nuclear charge.

In Paper V we derive inequalities for moments of the real part and the modulus of the eigen¬values of Schrödinger operators with complex-valued potentials.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. vii, 28 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 07:03
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-4344 (URN)978-91-7178-626-5 (ISBN)
Public defence
2007-05-09, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 09:00
Opponent
Supervisors
Note
QC 20100708Available from: 2007-04-25 Created: 2007-04-25 Last updated: 2010-07-08Bibliographically approved

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