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Eigenvalue estimates for Schrodinger operators on metric trees
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2011 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 226, no 6, 5165-5197 p.Article in journal (Refereed) Published
Abstract [en]

We consider Schrodinger 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.

Place, publisher, year, edition, pages
2011. Vol. 226, no 6, 5165-5197 p.
Keyword [en]
Schrodinger operator, Metric tree, Eigenvalue estimate, Lieb-Thirring inequality, Cwikel-Lieb-Rozenblum inequality
National Category
URN: urn:nbn:se:kth:diva-31911DOI: 10.1016/j.aim.2011.01.001ISI: 000288234600018ScopusID: 2-s2.0-79952043139OAI: diva2:406868
Swedish Research Council
QC 20110328Available from: 2011-03-28 Created: 2011-03-28 Last updated: 2011-03-28Bibliographically approved

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Ekholm, Tomas
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