References
- Courant R, Hilbert D. Methods of mathematical physics. Vol. 1. New York (NY): Wiley-Interscience; 1953.
- Arrieta JM, Hale JK, Han Q. Eigenvalue problems for non-smoothly perturbed domains. J Differential Equations. 1991;91:24–52. doi: 10.1016/0022-0396(91)90130-2
- Borisov D, Pankrashkin K. Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. J Phys A. 2013;46: 18 pp. Article 235203. doi: 10.1088/1751-8113/46/23/235203
- Cardone G, Nazarov S, Perugia C. A gap in the essential spectrum of a cylindrical waveguide with a periodic perturbation of the surface. Math Nachr. 2010;283:1222–1244. doi: 10.1002/mana.200910025
- Chechkin GA, Cioranescu D, Damlamian A, et al. On boundary value problem with singular inhomogeneity concentrated on the boundary. J Math Pures Appl. 2012;98:115–138. doi: 10.1016/j.matpur.2011.11.002
- Hempel R, Seco L, Simon B. The essential spectrum of Neumann Laplacians on some bounded singular domains. J Funct Anal. 1991;102:448–483. doi: 10.1016/0022-1236(91)90130-W
- Sanchez-Palencia E. Nonhomogeneous media and vibration theory. Berlin: Springer-Verlag; 1980.
- Cardone G, Khrabustovskyi A. Neumann spectral problem in a domain with very corrugated boundary. J Differential Equations. 2015;259(6):2333–2367. doi: 10.1016/j.jde.2015.03.031
- Pavlov BS. Extensions theory and explicitly solvable models. Russian Math Surveys. 1987;42(6):127–168. doi: 10.1070/RM1987v042n06ABEH001491
- Popov IYu. The extension theory and localization of resonances for the domain of trap type. Mat Sb. 1990;181(10):1366–1390. English: Mathematics of the USSR-Sbornik. 1992;71(1):209–234.
- Popov IYu. The resonator with narrow slit and the model based on the operator extensions theory. J Math Phys. 1992;33(11):3794–3801. doi: 10.1063/1.529877
- Popov IYu, Popova SL. The extension theory and resonances for a quantum waveguide. Phys Lett A. 1993;173:484–488. doi: 10.1016/0375-9601(93)90162-S
- Popov IYu, Popova SL. Zero-width slit model and resonances in mesoscopic systems. Europhys Lett. 1993;24(5):373–377. doi: 10.1209/0295-5075/24/5/009
- Popov IYu, Popova SL. Eigenvalues and bands imbedded in the continuous spectrum for a system of resonators and a waveguide: solvable model. Phys Lett A. 1996;222:286–290. doi: 10.1016/0375-9601(96)00643-3
- Gugel Yu.V, Popov IYu, Popova SL. Hydrotron: creep and slip. Fluid Dynam Res. 1996;18(4):199–210. doi: 10.1016/0169-5983(96)00009-3
- Melikhova AS, Popov IY. Spectral problem for solvable model of bent nanopeapod. Appl Anal. 2017;96(2):215–224. doi: 10.1080/00036811.2015.1120289
- Vorobiev AM, Bagmutov AS, Popov AI. On formal asymptotic expansion of resonance for quantum waveguide with perforated semitransparent barrier. Nanosys Phys Chem Math. 2019;10(4):415–419. doi: 10.17586/2220-8054-2019-10-4-415-419
- Birman MS, Solomyak MZ. Spectral theory of self-adjoint operators in Hilbert space. Dordrecht: D. Reidel Publishing Company; 1986.
- Behrndt J. Elliptic boundary value problems with k-dependent boundary conditions. J Differential Equations. 2010;249:2663–2687. doi: 10.1016/j.jde.2010.05.012
- Zangeneh-Nejad F, Fleury R. Active times for acoustic metamaterials. Rev Phys. 2019;4:100031. doi: 10.1016/j.revip.2019.100031