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Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Department of Physics, Princeton University.
Department of Physics, Princeton University.
2006 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 77, no 3, 309-316 p.Article in journal (Refereed) Published
Abstract [en]

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrodinger operator with a complex-valued potential.

Place, publisher, year, edition, pages
2006. Vol. 77, no 3, 309-316 p.
Keyword [en]
Schrodinger operator; Lieb-Thirring inequalities; complex potential
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-7030DOI: 10.1007/s11005-006-0095-1ISI: 000240126700007Scopus ID: 2-s2.0-33748086051OAI: oai:DiVA.org:kth-7030DiVA: diva2:11907
Note
QC 20100708Available from: 2007-04-25 Created: 2007-04-25 Last updated: 2010-07-08Bibliographically 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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