R. R. Gadyl'shin, “Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator”, Russian Math. Surveys, 52:1 (1997), 1

Citation in format AMSBIB

\Bibitem{Gad97}

\by R.~R.~Gadyl'shin

\paper Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator

\jour Russian Math. Surveys

\yr 1997

\vol 52

\issue 1

\pages 1--72

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This publication is cited in the following 36 articles:

I. Y. Popov, I. V. Blinova, A. I. Popov, “Completeness of Resonance States and Weyl Asymptotics of Resonances for Quantum Graphs”, Complex Anal. Oper. Theory, 19:3 (2025)
A. G. Belolipetskaia, I. Yu. Popov, “Influence of quantum graph parameters on the asymptotics of the number of resonances”, Chelyab. fiz.-matem. zhurn., 9:4 (2024), 682–688
E. S. Trifanova, A. S. Bagmutov, V. G. Katasonov, I. Yu. Popov, “Asymptotic expansions of resonances for waveguides coupled through converging windows”, Chelyab. fiz.-matem. zhurn., 8:1 (2023), 72–82
A. S. Bagmutov, E. S. Trifanova, I. Y. Popov, “Resonator with a Sorrugated Boundary: Numerical Results”, Phys. Part. Nuclei Lett., 20:2 (2023), 96
M. J. A. Smith, P. A. Cotterill, D. Nigro, W. J. Parnell, I. D. Abrahams, “Asymptotics of the meta-atom: plane wave scattering by a single Helmholtz resonator”, Phil. Trans. R. Soc. A., 380:2237 (2022)
Belolipetskaya A.G., Boitsev A.A., Fassari S., Popov I.Y., “3D Helmholtz Resonator With Two Close Point-Like Windows: Regularisation For Dirichlet Case”, Int. J. Geom. Methods Mod. Phys., 18:10 (2021), 2150153
Vorobiev A.M., “Resonance Asymptotics For Quantum Waveguides With Semitransparent Multi-Perforated Wall”, Nanosyst.-Phys. Chem. Math., 12:4 (2021), 462–471
Blinova V I., Popov I.Y., Popov I A., “Resonance States Completeness For Relativistic Particle on a Sphere With Two Semi-Infinite Lines Attached”, J. King Saud Univ. Sci., 32:1 (2020), 836–841
Vorobiev A.M., Trifanova E.S., Popov I.Y., “Resonance Asymptotics For a Pair Quantum Waveguides With Common Semitransparent Perforated Wall”, Nanosyst.-Phys. Chem. Math., 11:6 (2020), 619–627
V. Kozlov, J. Rossmann, “On the Nonstationary Stokes System in a Cone ($L_p$ Theory)”, J. Math. Fluid Mech., 22:3 (2020)
Gerasimov D., Popov I., Blinova I., Popov A., “Incompleteness of Resonance States For Quantum Ring With Two Semi-Infinite Edges”, Anal. Math. Phys., 9:3 (2019), 1287–1302
Vorobiev A.M., Bagmutov A.S., Popov I A., “on Formal Asymptotic Expansion of Resonance For Quantum Waveguide With Perforated Semitransparent Barrier”, Nanosyst.-Phys. Chem. Math., 10:4 (2019), 415–419
Gerasimov D.A., Popov I.Y., “Completeness of Resonance States For Quantum Graph With Two Semi-Infinite Edges”, Complex Var. Elliptic Equ., 63:7-8, SI (2018), 996–1010
Popov I.Yu., “Resonance States Completeness For a Model of the Helmholtz Resonator With Line-Like Window”, Appl. Math. E-Notes, 17 (2017), 157–163
Popov A.I., Popov I.Y., Gerasimov D.A., “Resonance State Completeness Problem For Quantum Graph”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), AIP Conference Proceedings, 1863, eds. Simos T., Tsitouras C., Amer Inst Physics, 2017, UNSP 390002-1
I.Y. Popov, A.I. Popov, “Line with attached segment as a model of Helmholtz resonator: Resonant states completeness”, Journal of King Saud University - Science, 29:1 (2017), 133
Habib Ammari, Hai Zhang, “A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators”, Commun. Math. Phys, 2015
Vorobiev A.M., Popov I.Yu., “Model of Quantum Dot and Resonant States For the Helmholtz Resonator”, 2Nd International School and Conference Saint-Petersburg Open on Optoelectronics, Photonics, Engineering and Nanostructures (Spbopen2015), Journal of Physics Conference Series, 643, IOP Publishing Ltd, 2015, 012097
Gadyl'shin R.R., “On Regular and Singular Perturbations of the Eigenelements of the Laplacian”, Analytic Methods, Integral Methods in Science and Engineering, 1, 2010, 135–148
Trifanova, ES, “Resonance phenomena in curved quantum waveguides coupled via windows”, Technical Physics Letters, 35:2 (2009), 180