Infinite quantum graphs |
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| Authors: | A S Kostenko M M Malamud H Neidhardt P Exner |
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| Institution: | 1.Faculty of Mathematics,University of Vienna,Vienna,Austria;2.Department of Partial Differential Equations, Institute of Applied Mathematics and Mechanics,National Academy of Sciences of Ukraine,Slavyansk,Ukraine;3.Weierstrass Institute for Applied Analysis and Stochastics,Berlin,Germany;4.Doppler Institute for Mathematical Physics and Applied Mathematics,Czech Technical University,Prague,Czechia;5.Department of Theoretical Physics, NPI,Academy of Sciences,Prague,Czechia |
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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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