Schrödinger Operators on Graphs and Branched Manifolds

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References

[1] Y. V. Pokorny, O. M. Penkin, V. L. Pryadier, A. V. Borovskikh, K. P. Lazarev and S. A. Shabrov, “Differential Equations on Geometric Graphs,” M. FIZMATLIT, 2004.

[2] V. L. Chernyshev and A. I. Shafarevich, “Semiclassical Spectrum of the Schrodinger Operator on a Geometric Graph,” Mathematical Notes, Vol. 82, No. 3-4, 2007, pp. 542-554. http://dx.doi.org/10.1134/S0001434607090313

[3] O. M. Penkin and Y. V. Pokornyi, “On Some Qualitative Properties of Equations for the One-Dimensional CW-complex,” Mathematical Notes, Vol.59, No. 5, 1996, pp. 562-565. http://dx.doi.org/10.1007/BF02308827

[4] A. A. Tolchennikov, V. L. Chernyshev and A. I. Shafarevich, “Asymptotic Properties and Classical Dynamical Systems in Quantum Problems on Singular Spaces,” Nelineinaya Dinamika, Vol. 6, No. 3, 2010, pp. 623-638.

[5] G. G. Amosov and V. Z. Sakbaev, “On Self-Adjoint Extensions of Schrodinger Operators Degenerating on a Pair of Half-Lines and the Corresponding Markovian Cocycles,” Mathematical Notes, Vol. 76, No. 3, 2004, pp. 315-322.

http://dx.doi.org/10.1023/B:MATN.0000043458.91218.7b

[6] V. Z. Sakbaev and O. G. Smolyanov, “Dynamics of a Quantum Particle with Discontinuous Position-Dependent Mass,” Doklady Mathematics, Vol. 82, No. 1, 2010, pp. 630-633. http://dx.doi.org/10.1134/S1064562410040332

[7] V. Z. Sakbaev and O. G. Smolyanov, “Diffusion and Quantum Dynamics on Graphs,” Doklady Mathematics, Vol. 88, No. 1, 2013, pp. 404-408. http://dx.doi.org/10.1134/S1064562413040108

[8] M. Gadella, S. Kuru and J. Negro, “Self-Adjoint Hamiltonians with a Mass Jump: General Matching Conditions,” Physics Letters A, 2007, Vol. 362, No. 4, pp. 265-268. http://dx.doi.org/10.1016/j.physleta.2006.10.029

[9] M. Reed and B. Simon, “Methods of Modern Mathematical Physics ‘1. Functional Analysis’,” Academic Press, New York London, 1972.

[10] T. Kato, “Perturbation Theory for Linear Operators,” Springer-Verlag, Berlin, Heidelberg, New York, 1966.

[11] N. Dunford and J. T. Schwartz, “Linear Operators ‘Part I: General Theory’,” Interscience Publishers, New York, London, 1958.

[12] G. N. Jakovlev, “Traces of Functions in the Space on Piecewise Smooth Surfaces,” Mathematics of the USSR-Sbornik, Vol. 3, No. 4, 1967, pp. 481-497. http://dx.doi.org/10.1070/SM1967v003n04ABEH002758