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Schrödinger operators on graphs and geometry. III. General vertex conditions and counterexamples
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0003-3256-6968
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22018 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 10, article id 102104Article in journal (Refereed) Published
Abstract [en]

Schrödinger operators on metric graphs with general vertex conditions are studied. Explicit spectral asymptotics is derived in terms of the spectrum of reference Laplacians. A geometric version of the Ambartsumian theorem is proven under the assumption that the vertex conditions are asymptotically properly connecting and asymptotically standard. By constructing explicit counterexamples, it is shown that the geometric Ambartsumian theorem does not hold in general without additional assumptions on the vertex conditions.

Place, publisher, year, edition, pages
2018. Vol. 59, no 10, article id 102104
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Mathematics
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URN: urn:nbn:se:su:diva-162757DOI: 10.1063/1.5039459ISI: 000449104100019OAI: oai:DiVA.org:su-162757DiVA, id: diva2:1274800
Available from: 2019-01-03 Created: 2019-01-03 Last updated: 2020-02-06Bibliographically approved

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