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Rayleigh estimates for differential operators on graphs
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 4, no 2, 211-219 p.Article in journal (Refereed) Published
Abstract [en]

We study the spectral gap, i.e. the distance between the two lowest eigenvalues for Laplace operators on metric graphs. A universal lower estimate for the spectral gap is proven and it is shown that it is attained if the graph is formed by just one interval. Uniqueness of the minimizer allows to prove a geometric version of the Ambartsumian theorem derived originally for Schrodinger operators.

Place, publisher, year, edition, pages
2014. Vol. 4, no 2, 211-219 p.
Keyword [en]
Quantum graph, Eulerian path, spectral gap
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-107209DOI: 10.4171/JST/67ISI: 000340040100001OAI: oai:DiVA.org:su-107209DiVA: diva2:743975
Note

AuthorCount:2;

Available from: 2014-09-05 Created: 2014-09-05 Last updated: 2017-12-05Bibliographically approved

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Kurasov, Pavel
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