Published April 1, 2011
| Version Submitted
Journal Article
Open
Eigenvalue estimates for Schrödinger operators on metric trees
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1.
Royal Institute of Technology
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2.
Princeton University
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3.
Polytechnic University of Turin
Abstract
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.
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.Attached Files
Submitted - 0710.5500.pdf
Files
0710.5500.pdf
Additional details
Identifiers
- Eprint ID
- 77398
- Resolver ID
- CaltechAUTHORS:20170512-094610802
Related works
- Describes
- https://arxiv.org/abs/0710.5500 (URL)
Funding
- Vetenskapsrådet/Swedish Research Council
- Deutscher Akademischer Austauschdienst (DAAD)
- D/06/49117
- European Science Foundation
- Swedish Foundation for International Cooperation in Research and Higher Education (STINT)
Dates
- Created
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2017-05-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
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