V. V. Grushin, “On the Eigenvalues of Finitely Perturbed Laplace Operators in Infinite Cylindrical Domains”, Mat. Zametki, 75:3 (2004), 360–371; Math. Notes, 75:3 (2004), 331

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Matematicheskie Zametki, 2004, Volume 75, Issue 3, Pages 360–371
DOI: https://doi.org/10.4213/mzm40 (Mi mzm40)

This article is cited in 35 scientific papers (total in 35 papers)

On the Eigenvalues of Finitely Perturbed Laplace Operators in Infinite Cylindrical Domains

V. V. Grushin

Moscow State Institute of Electronics and Mathematics

Full-text PDF (225 kB) Citations (35)

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DOI: https://doi.org/10.4213/mzm40

Abstract: In this paper, sufficient conditions for the existence of eigenvalues of a finitely perturbed Laplace operator in an infinite cylindrical domain and their asymptotics in the small parameter are given. Similar questions for tubes, i.e., deformed cylinders, are also considered.

Received: 26.05.2003

English version:
Mathematical Notes, 2004, Volume 75, Issue 3, Pages 331–340
DOI: https://doi.org/10.1023/B:MATN.0000023312.41107.72

Bibliographic databases:

UDC: 517.958 517.95

Language: Russian

Citation: V. V. Grushin, “On the Eigenvalues of Finitely Perturbed Laplace Operators in Infinite Cylindrical Domains”, Mat. Zametki, 75:3 (2004), 360–371; Math. Notes, 75:3 (2004), 331–340

Citation in format AMSBIB

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This publication is cited in the following 35 articles:

S. A. Nazarov, “The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides”, Sb. Math., 212:7 (2021), 965–1000
S. A. Nazarov, “Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides”, Izv. Math., 84:6 (2020), 1105–1160
Bruneau V. Miranda P. Parra D. Popoff N., “Eigenvalue and Resonance Asymptotics in Perturbed Periodically Twisted Tubes: Twisting Versus Bending”, Ann. Henri Poincare, 21:2 (2020), 377–403
Bagmutov A.S., Popov I.Y., “Window-Coupled Nanolayers: Window Shape Influence on One-Particle and Two-Particle Eigenstates”, Nanosyst.-Phys. Chem. Math., 11:6 (2020), 636–641
Barseghyan D., Khrabustovskyi A., “Spectral Estimates For Dirichlet Laplacian on Tubes With Exploding Twisting Velocity”, Oper. Matrices, 13:2 (2019), 311–322
Cardone G., Durante T., Nazarov S.A., “Embedded Eigenvalues of the Neumann Problem in a Strip With a Box-Shaped Perturbation”, J. Math. Pures Appl., 112 (2018), 1–40
Piat V.Ch., Nazarov S.A., Taskinen J., “Embedded Eigenvalues Forwater-Waves in Athree-Dimensional Channel With Athin Screen”, Q. J. Mech. Appl. Math., 71:2 (2018), 187–220
S. A. Nazarov, “Transmission of waves through a small aperture in the cross-wall in an acoustic waveguide”, Siberian Math. J., 59:1 (2018), 85–101
Bruneau V., Miranda P., Popoff N., “Resonances Near Thresholds in Slightly Twisted Waveguides”, Proc. Amer. Math. Soc., 146:11 (2018), 4801–4812
S. A. Nazarov, “Asymptotics of eigenvalues in spectral gaps of periodic waveguides with small singular perturbations”, J. Math. Sci. (N. Y.), 243:5 (2019), 746–773
S. A. Nazarov, “Various manifestations of Wood anomalies in locally distorted quantum waveguides”, Comput. Math. Math. Phys., 58:11 (2018), 1838–1855
S. A. Nazarov, “Almost standing waves in a periodic waveguide with a resonator and near-threshold eigenvalues”, St. Petersburg Math. J., 28:3 (2017), 377–410
Bikmetov A.R. Gadyl'shin R.R., “On local perturbations of waveguides”, Russ. J. Math. Phys., 23:1 (2016), 1–18
S. A. Nazarov, “Transmission Conditions in One-Dimensional Model of a Rectangular Lattice of Thin Quantum Waveguides”, J Math Sci, 219:6 (2016), 994
S. A. Nazarov, “Scattering anomalies in a resonator above the thresholds of the continuous spectrum”, Sb. Math., 206:6 (2015), 782–813
Nazarov S.A., “Near-threshold effects of the scattering of waves in a distorted elastic two-dimensional waveguide”, Pmm-J. Appl. Math. Mech., 79:4 (2015), 374–387
Exner P. Kovarik H., Quantum Waveguides, Theoretical and Mathematical Physics, Springer-Verlag Berlin, 2015, 1–382
Briet Ph., Kovarik H., Raikov G., “Scattering in Twisted Waveguides”, J. Funct. Anal., 266:1 (2014), 1–35
S. A. Nazarov, “Bounded solutions in a $\mathrm{T}$ -shaped waveguide and the spectral properties of the Dirichlet ladder”, Comput. Math. Math. Phys., 54:8 (2014), 1261–1279
Cardone G., Nazarov S.A., Ruotsalainen K., “Bound States of a Converging Quantum Waveguide”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 47:1 (2013), 305–315

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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