Visibility of quantum graph spectrum from the vertices

Christian Kühn; Jonathan Rohleder

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arXiv · 1602.03394

Visibility of quantum graph spectrum from the vertices

Christian Kühn·Jonathan Rohleder

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Abstract

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.

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BibTeX RIS

Christian Kühn, Jonathan Rohleder. 2016-02-10. Visibility of quantum graph spectrum from the vertices. https://arxiv.org/abs/1602.03394

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