![]() ![]() ![]() Press, Cambridge (1989)ĭavies, E.B.: Large deviations for heat kernels on graphs. Press, Cambridge (2003)ĭavies, E.B.: Heat Kernels and Spectral Theory. 14(1), 21–38 (2011)ĭavidoff, G., Sarnak, P., Valette, A.: Elementary Number Theory, Group Theory and Ramanujan Graphs. de France, Paris (1998)Ĭolin de Verdiére, Y., Torki-Hamza, N., Truc, F.: Essential self-adjointness for combinatorial Schrödinger operators II-metrically non complete graphs. 37, 元29–元35 (2004)Ĭheon, T., Exner, P., Turek, O.: Approximation of a general singular vertex coupling in quantum graphs. Media 7(3), 483–501 (2012)Ĭattaneo, C.: The spectrum of the continuous Laplacian on a graph. 2000(71), 1–24 (2000)Ĭarlson, R.: Dirichlet to Neumann maps for infinite quantum graphs. 254, 3835–3902 (2013)Ĭarlson, R.: Nonclassical Sturm–Liouville problems and Schrödinger operators on radial trees. 20, 1–70 (2008)Ĭarlone, R., Malamud, M., Posilicano, A.: On the spectral theory of Gesztezy–Šeba realizations of 1-D Dirac operators with point interactions on discrete set. 21, 929–945 (2009)īrüning, J., Geyler, V., Pankrashkin, K.: Spectra of self-adjoint extensions and applications to solvable Schrödinger operators. Soc, Providence, RI (2013)īreuer, J., Frank, R.: Singular spectrum for radial trees. Soc., Providence, RI (2006)īerkolaiko, G., Kuchment, P.: Introduction to Quantum Graphs. 17, 259–271 (2015)īerkolaiko, G., Carlson, R., Fulling, S., Kuchment, P.: Quantum graphs and their applications. 17, 1996–2007 (1999)īauer, F., Keller, M., Wojciechowski, R.K.: Cheeger inequalities for unbounded graph Laplacians. 36, 93–112 (2004)Īxmann, W., Kuchment, P., Kunyansky, L.: Asymptotic methods for thin high contrast 2D PBG materials. Art ID 165206Īmovilli, C., Leys, F., March, N.: Electronic energy spectrum of two-dimensional solids and a chain of C atoms from a quantum network model. 5(3), 227–277 (2018)Īlonso-Ruiz, P., Kelleher, D.J., Teplyaev, A.: Energy and Laplacian on Hanoi-type fractal quantum graphs. arXiv:1712.00385Īlonso-Ruiz, P., Freiberg, U., Kigami, J.: Completely symmetric resistance forms on the stretched Sierpinski gasket. B 27, 1541–1557 (1985)Īlonso-Ruiz, P.: Explicit formulas for heat kernels on diamond fractals. A percolation approach to the effects of disorder. ID 102102 (2010)Īlexander, S.: Superconductivity of networks. Soc., Providence, RI (2005)Īlbeverio, S., Kostenko, A., Malamud, M.: Spectral theory of semi-bounded Sturm–Liouville operators with local interactions on a discrete set. ![]() 228, 144–188 (2005)Īlbeverio, S., Gesztesy, F., Hoegh-Krohn, R., Holden, H.: Solvable Models in Quantum Mechanics, 2nd edn, with an appendix by P. 264, 371–389 (2006)Īlbeverio, S., Brasche, J.F., Malamud, M.M., Neidhardt, H.: Inverse spectral theory for symmetric operators with several gaps: scalar-type Weyl functions. Fields 136, 363–394 (2005)Īizenman, M., Sims, R., Warzel, S.: Absolutely continuous spectra of quantum tree graphs with weak disorder. You can now fill in as much detail as you need to verify that the function $f$ is indeed a bijection.Aizenman, M., Sims, R., Warzel, S.: Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Geometrically it should be clear that the indicated map is a bijection, but one can write the map down explicitly and verify directly that you do indeed have a bijection to the interior of the unit disk in the $xy$-plane. ![]()
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