# Spectral Theory of Infinite Quantum Graphs

@article{Exner2018SpectralTO, title={Spectral Theory of Infinite Quantum Graphs}, author={Pavel Exner and Aleksey Kostenko and Mark M. Malamud and Hagen Neidhardt}, journal={Annales Henri Poincar{\'e}}, year={2018}, volume={19}, pages={3457-3510} }

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection together with spectral theory of (unbounded) discrete Laplacians on…

## 30 Citations

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