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Infinite quantum graphs

Abstract

Infinite quantum graphs with δ-interactions at vertices are studied without any assumptions on the lengths of edges of the underlying metric graphs. A connection between spectral properties of a quantum graph and a certain discrete Laplacian given on a graph with infinitely many vertices and edges is established. In particular, it is shown that these operators are self-adjoint, lower semibounded, nonnegative, discrete, etc. only simultaneously.

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Correspondence to A. S. Kostenko.

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Original Russian Text © A.S. Kostenko, M.M. Malamud, H. Neidhardt, P. Exner, 2017, published in Doklady Akademii Nauk, 2017, Vol. 472, No. 3, pp. 253–258.

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Kostenko, A.S., Malamud, M.M., Neidhardt, H. et al. Infinite quantum graphs. Dokl. Math. 95, 31–36 (2017). https://doi.org/10.1134/S1064562417010136

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  • DOI: https://doi.org/10.1134/S1064562417010136