References
- Berkolaiko G, Kuchment P. Introduction to quantum graphs. Providence Rhode Island: AMS; 2013. (Mathematical Surveys and Monographs; 186).
- Exner P, Keating JP, Kuchment P, et al., editors. Analysis on graphs and its applications. In: Proceedings of symposia in pure mathematics. Vol. 77. Providence, Rhode Island: AMS; 2008.
- Korotyaev E, Lobanov I. Schrödinger operators on zig-zag nano-tubes. Ann Henri Puancaré. 2007;8(6): 1151–1176. doi: 10.1007/s00023-007-0331-y
- Korotyaev E, Saburova N. Scattering on periodic metric graphs. 2015. arXiv:1507.06441v1 [math.SP] 23.
- Kuchment P. Quantum graphs: I. Some basic structures. Waves Random Media. 2007;14:107–128. doi: 10.1088/0959-7174/14/1/014
- Kuchment P. Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs. J Phys A. 2005;38:4887–4900. doi: 10.1088/0305-4470/38/22/013
- Kuchment P, Post O. On the spectra of carbon nano-structures. Comm Math Phys. 2007;275(3):805–826. doi: 10.1007/s00220-007-0316-1
- Kuchment P, Kuniansky A. Spectral properties of high contrast band-gap materials and operators on graphs. Exp Math. 1999;8(1):1–28. doi: 10.1080/10586458.1999.10504384
- Kuchment P, Vainberg B. On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators. Commun Math Phys. 2006;268(3):673–686. doi: 10.1007/s00220-006-0105-2
- Akduman S, Pankov A. Schrödinger operators with locally integrable potentials on infinite metric graphs. Appl Anal. 2017;96:2149–2161. Available from: http://dx.doi.org/10.1080/00036811.2016.1207247
- Rabinovich V. On the essential spectrum of quantum graphs. Integr Equ Oper Theory. 2017;88:339–362. doi: 10.1007/s00020-017-2386-6
- Barrera-Figueroa V, Rabinovich VS, Maldonado Rosas M. Numerical estimates of the essential spectra of quantum graphs with delta-interactions at vertices. Appl Anal. 2019;98(1-2):458–482. Available from: https://doi.org/10.1080/00036811.2017.1419201
- Agranovich MS, Vishik MI. Elliptic problems with a parameter and parabolic problems of general forms. Uspekhi Mat Nauk. 1964;219:63–161; English trans. Russian Math. Surveys. 1964;19:53–157.
- Agranovich MS. Elliptic boundary problem. In: Agranovich MS, Egorov YuV, Shubin MA, editors. Partial differential equations IX, Elliptic boundary value problems. Vol. IX. Heidelberg, New York, Dordrecht, London: Springer; 1996.
- Agranovich MS. Sobolev spaces, their generalizations, and elliptic problems in smooth and Lipschitz domains. Heidelberg, New York, Dordrecht, London: Springer; 2015.
- Denk R, Volevich L. Elliptic boundary value problems with large parameter for mixed order systems. Amer Math Soc Transl. 2002;206:29–64.
- Denk R, Hieber M, Prüss J. R-boundness, Fourier multipliers and problems of elliptic and parabolic type. Mem Amer Math Soc. 2003;166:1–113.
- Grubb G. Functional calculus of boundary value problems. Berlin, Heidelberg, New York: Springer Verlag; 1966.
- Volpert V. Elliptic problems with a parameter in unbounded domains. Adv Differential Equations. 2007;12(5):573–600.
- von Below J. Classical solvability of linear parabolic equations on networks. J Differential Equations. 1988;72:316–337. doi: 10.1016/0022-0396(88)90158-1
- Thanou D, Xiaowen D, Kressner D, et al. Learning heat diffusion graphs. IEEE Trans Signal Inform Process Netw. 2017;3:3.
- Chung S-Y, Chung Y-S, Kim J-H. Diffusion and elastic equations on networks. Publ RIMS Kyoto Univ. 2007;43:699–725. doi: 10.2977/prims/1201012039
- Cardanobile S. Diffusion systems and heat equations on networks. arXiv:0807.2362v1 [math.FA] 15 Jul 2008.
- Grubb G. Parabolic pseudodifferential boundary problems and applications. Berlin–Heidelberg–New York: Springer-Verlag; 1991. p. 46–117. (Lecture Notes in Mathematics; 1495).
- Eidel'man SD. Parabolic equations. In: Egorov YuV, Shubin MA, editors. Partial differential equations. VI. Berlin: Springer; 1994. p. 205–316. (Encyclopaedia of Mathematical Sciences; 63).
- Solonnikov VA. Apriori estimates for solutions of second-order equations of parabolic type. Trudy Mat Inst Steklov. 1964;70:133–212. (Russian).
- Rabinovich VS, Roch S, Silbermann B. Limit operators and its applications in the operator theory. Basel, Boston, Berlin: Birkhäuser Velag, 2004. (Operator theory: advances and applications; 150).
- Gohberg I, Sigal EI. Operator generalization of the theorem on the logarithmical resedue and Rouche's theorem. Mat Sb. 1971;84(4):607–629.