Rayleigh estimates for differential operators on graphs
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
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.
Quantum graph, Eulerian path, spectral gap
IdentifiersURN: urn:nbn:se:su:diva-107209DOI: 10.4171/JST/67ISI: 000340040100001OAI: oai:DiVA.org:su-107209DiVA: diva2:743975