Email this article Infinite quantum graphs
- Authors: Kostenko A.S.1, Malamud M.M.2, Neidhardt H.3, Exner P.4,5
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Affiliations:
- Faculty of Mathematics
- Department of Partial Differential Equations, Institute of Applied Mathematics and Mechanics
- Weierstrass Institute for Applied Analysis and Stochastics
- Doppler Institute for Mathematical Physics and Applied Mathematics
- Department of Theoretical Physics, NPI
- Issue: Vol 95, No 1 (2017)
- Pages: 31-36
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224725
- DOI: https://doi.org/10.1134/S1064562417010136
- ID: 224725
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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.
About the authors
A. S. Kostenko
Faculty of Mathematics
Author for correspondence.
Email: oleksiy.kostenko@univie.ac.at
Austria, Osckar-Morgenstern-Platz 1, Vienna, 1090
M. M. Malamud
Department of Partial Differential Equations, Institute of Applied Mathematics and Mechanics
Email: oleksiy.kostenko@univie.ac.at
Ukraine, ul. Dobrovol’skogo 1, Slavyansk, 84100
H. Neidhardt
Weierstrass Institute for Applied Analysis and Stochastics
Email: oleksiy.kostenko@univie.ac.at
Germany, Berlin
P. Exner
Doppler Institute for Mathematical Physics and Applied Mathematics; Department of Theoretical Physics, NPI
Email: oleksiy.kostenko@univie.ac.at
Czech Republic, Prague; Prague
