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Visibility of quantum graph spectrum from the vertices

Research paper by Christian Kühn, Jonathan Rohleder

Indexed on: 10 Feb '16Published on: 10 Feb '16Published in: Mathematics - Spectral Theory



Abstract

We investigate the relation between the eigenvalues of the Kirchhoff Laplacian on a finite metric graph and a corresponding Titchmarsh-Weyl function. We establish an explicit, optimal bound in terms of the edge lengths and the connectivity of the graph such that all eigenvalues below that bound are visible for the Titchmarsh-Weyl function. This bound corresponds to the smallest real resonance of the graph.