References
- Kirchhoff GR. Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Ströme gefürt wird [On the solution of the equations to which one is led in the investigation of the linear distribution of galvanic currents]. Ann. Phys. Chem. 1847;72:497–508.
- Berkolaiko G, Kuchment P. Introduction to quantum graphs. Providence (RI): American Mathematical Society; 2013.
- Blank J, Exner P, Havliček M. Hilbert space operators in quantum physics. New York (NY): Springer; 2008.
- Mehmeti F, von Below J, Nicaise S, editors. Partial differential equations on microstructures. Boca Raton (FL): CRC Press; 2001.
- Pokornyi YV, Penkin OM, Pryadiev VL, et al. Differential equations on geometric graphs. Moscow: Fizmatlit; 2005. Russian.
- von Below J. The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions. Lin. Algebra Appl. 2013;439:1792–1814.
- Kuchment P. Graph models for waves in thin structures. Waves Random Media. 2002;12:R1–R24.
- Kuchment P. Quantum graphs: I, some basic structures. Waves Random Media. 2004;14:S107–S128.
- Kuchment P. Quantum grephs: II, some spectral properties for infinite and combinatorial graphs. J. Phys. A: Math. Gen. 2005;38:4887–4900.
- Pokornyi YV, Pryadiev VL. Some problems in the qualitative Sturm--Liouville theory an a spatial network. Uspekhi Mat. Nauk 2004;59:115–150. translation in. Russian Math. Surveys. 2004;59:515–552. Russian.
- Cycon HL, Froese RG, Kirsch W, et al. Schrödinger operators in quantum mechanics and global geometry. Berlin: Springer; 1987.
- Simon B. Schrödinger semigroupes. Bull. Amer. Math. Soc. 1982;7:447–526.
- Agmon S. Bounds on exponential decay of eigenfunctions of Schrödinger operators. Lecture notes in mathematics. Vol. 1159. Berlin: Springer; 1985. pp. 1–38.
- Birman MS. Perturbations of quadratic forms and the spectrum of singular boundary value problems. DAN SSSR. 1959;125:471–474. Russian.
- Glazman I. Direct methods of qualitative spectral analysis of singular differential operators. Jerusalem: Israel program for scientific translations; 1965.
- Molchanov AM. On the discreteness of the spectrum conditions for self-adjoint differential operators of second order (Russian). Trudy Moskovskogo Matem. Ob-va. 1953;2:169–199.
- Kovaleva MO, Popov IY. On Molchanov’s condition for the spectrum discreteness of a quantum graph Hamiltonian with δ-coupling. Reports Math. Phys. 2015;76:171–178.
- Reed M, Simon B. Methods of modern mathematical physics: II, Fourier analysis, self-adjointness. San Diego (CA): Academic Press; 1975.