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Eigenvalue estimates for Schrödinger operators on metric trees

Ekholm, Tomas and Frank, Rupert L. and Kovařík, Hynek (2011) Eigenvalue estimates for Schrödinger operators on metric trees. Advances in Mathematics, 226 (6). pp. 5165-5197. ISSN 0001-8708.

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We consider Schrödinger operators on radial metric trees and prove Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.

Item Type:Article
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URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2011 Elsevier Inc. Received 11 October 2007, Accepted 3 January 2011, Available online 13 January 2011. Communicated by the Managing Editors of AIM. The authors are grateful to Robert Seiringer and Timo Weidl for several useful discussions, and to the organizers of the workshop ‘Analysis on Graphs’ at the Isaac Newton Institute in Cambridge for their kind invitation. This work has been supported by Vetenskapsrådet/Swedish Research Council (T.E.) and DAAD grant D/06/49117 (R.F.). Partial support by the ESF programme SPECT (T.E. and H.K.) and the DAAD-STINT PPP programme (R.F.) is gratefully acknowledged.
Funding AgencyGrant Number
Vetenskapsrådet/Swedish Research CouncilUNSPECIFIED
Deutscher Akademischer Austauschdienst (DAAD)D/06/49117
European Science FoundationUNSPECIFIED
Swedish Foundation for International Cooperation in Research and Higher Education (STINT)UNSPECIFIED
Subject Keywords:Schrödinger operatorMetric treeEigenvalue estimateLieb–Thirring inequalityCwikel–Lieb–Rozenblum inequality
Issue or Number:6
Record Number:CaltechAUTHORS:20170512-094610802
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Official Citation:Tomas Ekholm, Rupert L. Frank, Hynek Kovařík, Eigenvalue estimates for Schrödinger operators on metric trees, Advances in Mathematics, Volume 226, Issue 6, 2011, Pages 5165-5197, ISSN 0001-8708, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77398
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 23:38
Last Modified:09 Mar 2020 13:18

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