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Infinite quantum graphs

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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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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Osckar-Morgenstern-Platz 1, Vienna, 1090, Austria

    A. S. Kostenko

  2. Department of Partial Differential Equations, Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. Dobrovol’skogo 1, Slavyansk, 84100, Ukraine

    M. M. Malamud

  3. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    H. Neidhardt

  4. Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Prague, Czechia

    P. Exner

  5. Department of Theoretical Physics, NPI, Academy of Sciences, Prague, Czechia

    P. Exner

Authors
  1. A. S. Kostenko
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  2. M. M. Malamud
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  3. H. Neidhardt
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  4. P. Exner
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Corresponding author

Correspondence to A. S. Kostenko.

Additional information

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

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