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

Ekholm, Tomas and Frank, Rupert (2008) Lieb–Thirring inequalities on the half-line with critical exponent. European Mathematical Society, 10 (3). pp. 739-755. ISSN 1435-9855. https://resolver.caltech.edu/CaltechAUTHORS:20170531-151816388

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Abstract

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 tr (-d^2)/dr^2 -V)^y_- ≤ Cy,ɑʃ_(R+) (v(r)-1/_(4r)^2)^(y+(1+ɑ)/2_(r^ɑ dr) for any ɑ Є [0,1] and y ≥ (1 - ɑ)/2. This includes a Lieb–Thirring inequality in the critical endpoint case.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/ 10.4171/JEMS/128DOIArticle
http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=10&iss=3&rank=6PublisherArticle
https://arxiv.org/abs/math/0611247arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert0000-0001-7973-4688
Additional Information:© 2008 European Mathematical Society. Received December 6, 2006 and in revised form January 22, 2007. This work was partially supported by FCT Portugal, post-doc grant SFRH/BPD/23820/2005, (T.E.), by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) (R.F.), as well as through the ESF Scientific Programme in Spectral Theory and Partial Differential Equations (SPECT). The authors are grateful to the American Institute of Mathematics for the invitation to the workshop Low Eigenvalues of Laplace and Schrödinger Operators where this problem was brought up. R.F. would like to thank E.H. Lieb and R. Seiringer for the hospitality at Princeton University and for helpful discussions. Remarks by A. Hansson and A. Laptev are gratefully acknowledged.
Funders:
Funding AgencyGrant Number
Fundação para a Ciência e a Tecnologia (FCT)SFRH/BPD/23820/2005
Swedish Foundation for International Cooperation in Research and Higher Education (STINT)UNSPECIFIED
European Science FoundationUNSPECIFIED
Subject Keywords:Schrödinger operator, Lieb–Thirring inequalities, Hardy inequality
Issue or Number:3
Record Number:CaltechAUTHORS:20170531-151816388
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170531-151816388
Official Citation: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
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77867
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 Jun 2017 15:02
Last Modified:09 Mar 2020 13:18

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