![]() ![]() The main subject of our studies is precisely non-self-adjoint quantum graphs. Hussein, A., Krejcirik, D., and Siegl, P., “ Non-self-adjoint graphs,” Trans. If the theory of self-adjoint operators on metric graphs is rather well-understood, the corresponding theory of non-self-adjoint operators is in its incubatory stage. Post, O., Spectral Analysis on Graph-Like Spaces ( Springer Science & Business Media, 2012), Vol. and Naboko, S., “ Rayleigh estimates for differential operators on graphs,” J. B., Kurasov, P., Malenová, G., and Mugnolo, D., “ On the spectral gap of a quantum graph,” in Annales Henri Poincaré ( Springer, 2015), pp. ![]() and Kurasov, P., “ Symmetries of quantum graphs and the inverse scattering problem,” Adv. Band, R., Parzanchevski, O., and Ben-Shach, G., “ The isospectral fruits of representation theory: Quantum graphs and drums,” J. It appeared that symmetries of the underlying metric graphs play a very important role in constructing counterexamples and proving spectral estimates. Kurasov, P., Spectral Theory of Quantum Graphs and Inverse Problems ( Birkhäuser) (to be published). Kurasov, P., “ Schrödinger operators on graphs and geometry. and Schrader, R., “ Kirchhoff’s rule for quantum wires,” J. and Smilansky, U., “ Can one hear the shape of a graph?,” J. and Kuchment, P., Introduction to Quantum Graphs ( American Mathematical Society, 2013), Vol. This is one of the most rapidly growing areas of modern mathematical physics due to its important applications in physics and applied sciences as well as interesting mathematical problems that emerge. Our paper is devoted to spectral theory of quantum graphs-ordinary differential operators on metric graphs. ![]()
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