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Visibility of quantum graph spectrum from the vertices
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0003-1354-5387
2018 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, no 9, article id 095204Article in journal (Refereed) Published
Abstract [en]

We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex conditions on a finite metric graph and a corresponding Titchmarsh–Weyl function (a parameter-dependent Neumann-to-Dirichlet map). We give a complete description of all real resonances, including multiplicities, in terms of the edge lengths and the connectivity of the graph, and apply it to characterize all eigenvalues which are visible for the Titchmarsh–Weyl function.

Place, publisher, year, edition, pages
2018. Vol. 51, no 9, article id 095204
Keyword [en]
quantum graph, resonance, Titchmarsh-Weyl function, Neumann-to-Dirichlet map, inverse problem
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-153940DOI: 10.1088/1751-8121/aaa884ISI: 000424355500002OAI: oai:DiVA.org:su-153940DiVA, id: diva2:1188912
Available from: 2018-03-08 Created: 2018-03-08 Last updated: 2018-03-20Bibliographically approved

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