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Mat. Zametki, 1997, Volume 62, Issue 6, Pages 950–953 (Mi mz1688)  

This article is cited in 23 scientific papers (total in 23 papers)

Brief Communications

The limit behavior of the spectrum for large parameter values in a model problem

A. A. Shkalikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

DOI: https://doi.org/10.4213/mzm1688

Full text: PDF file (267 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 1997, 62:6, 796–799

Bibliographic databases:

Received: 09.06.1997
Revised: 25.06.1997

Citation: A. A. Shkalikov, “The limit behavior of the spectrum for large parameter values in a model problem”, Mat. Zametki, 62:6 (1997), 950–953; Math. Notes, 62:6 (1997), 796–799

Citation in format AMSBIB
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\by A.~A.~Shkalikov
\paper The limit behavior of the spectrum for large parameter values in a model problem
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\yr 1997
\vol 62
\issue 6
\pages 950--953
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\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 6
\pages 796--799
\crossref{https://doi.org/10.1007/BF02355473}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Stepin, “On the spectral properties of the non-self-conjugate operator $i\varepsilon\dfrac{d^2}{dx^2}+q(x)$”, Russian Math. Surveys, 53:3 (1998), 639–641  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Redparth, P, “Spectral properties of non-self-adjoint operators in the semi-classical regime”, Journal of Differential Equations, 177:2 (2001), 307  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. A. V. D'yachenko, A. A. Shkalikov, “On a Model Problem for the Orr–Sommerfeld Equation with Linear Profile”, Funct. Anal. Appl., 36:3 (2002), 228–232  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. S. N. Tumanov, A. A. Shkalikov, “On the Spectrum Localization of the Orr–Sommerfeld Problem for Large Reynolds Numbers”, Math. Notes, 72:4 (2002), 519–526  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Davies, EB, “Non-self-adjoint differential operators”, Bulletin of the London Mathematical Society, 34 (2002), 513  crossref  mathscinet  zmath  isi  scopus  scopus
    6. A. A. Shkalikov, “Spectral Portraits of the Orr–Sommerfeld Operator with Large Reynolds Numbers”, Journal of Mathematical Sciences, 124:6 (2004), 5417–5441  mathnet  crossref  mathscinet  zmath
    7. Trefethen, LN, “Wave packet pseudomodes of variable coefficient differential operators”, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 461:2062 (2005), 3099  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Gunther, U, “MHD alpha(2)-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator”, Journal of Mathematical Physics, 46:6 (2005), 063504  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. S. V. Galtsev, A. I. Shafarevich, “Spectrum and Pseudospectrum of non-self-adjoint Schrödinger Operators with Periodic Coefficients”, Math. Notes, 80:3 (2006), 345–354  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. S. V. Galtsev, A. I. Shafarevich, “Quantized Riemann surfaces and semiclassical spectral series for a non-self-adjoint Schrödinger operator with periodic coefficients”, Theoret. and Math. Phys., 148:2 (2006), 1049–1066  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Roohian, H, “Semiclassical asymptotics of the spectrum of a nonselfadjoint operator on the sphere”, Russian Journal of Mathematical Physics, 16:2 (2009), 309  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. V. I. Pokotilo, A. A. Shkalikov, “Semiclassical Approximation for a Nonself-Adjoint Sturm–Liouville Problem with a Parabolic Potential”, Math. Notes, 86:3 (2009), 442–446  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. Rubinstein, J, “The Resistive State in a Superconducting Wire: Bifurcation from the Normal State”, Archive For Rational Mechanics and Analysis, 195:1 (2010), 117  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. A. I. Esina, A. I. Shafarevich, “Quantization Conditions on Riemannian Surfaces and the Semiclassical Spectrum of the Schrödinger Operator with Complex Potential”, Math. Notes, 88:2 (2010), 209–227  mathnet  crossref  crossref  mathscinet  isi  elib
    15. Roohian H., Shafarevich A.I., “Semiclassical Asymptotic Behavior of the Spectrum of a Nonselfadjoint Elliptic Operator on a Two-Dimensional Surface of Revolution”, Russian Journal of Mathematical Physics, 17:3 (2010), 328–333  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    16. Hari L.P., Rubinstein J., Sternberg P., “Kinematic and Dynamic Vortices in a Thin Film Driven by an Applied Current and Magnetic Field”, Physica D, 261 (2013), 31–41  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    17. Esina A.I. Shafarevich A.I., “Analogs of Bohr-Sommerfeld-Maslov Quantization Conditions on Riemann Surfaces and Spectral Series of Nonself-Adjoint Operators”, Russ. J. Math. Phys., 20:2 (2013), 172–181  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. A. I. Esina, A. I. Shafarevich, “Asymptotics of the Spectrum and Eigenfunctions of the Magnetic Induction Operator on a Compact Two-Dimensional Surface of Revolution”, Math. Notes, 95:3 (2014), 374–387  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    19. Tumanov S.N. Shkalikov A.A., “the Limit Spectral Graph in Semiclassical Approximation For the Sturm-Liouville Problem With Complex Polynomial Potential”, Dokl. Math., 92:3 (2015), 773–777  crossref  mathscinet  zmath  isi  scopus  scopus
    20. Kh. K. Ishkin, “Localization criterion for the spectrum of the Sturm–Liouville operator on a curve”, St. Petersburg Math. J., 28:1 (2017), 37–63  mathnet  crossref  mathscinet  isi  elib
    21. A. M. Savchuk, A. A. Shkalikov, “Spectral Properties of the Complex Airy Operator on the Half-Line”, Funct. Anal. Appl., 51:1 (2017), 66–79  mathnet  crossref  crossref  mathscinet  isi  elib
    22. D. V. Nekhaev, A. I. Shafarevich, “A quasiclassical limit of the spectrum of a Schrödinger operator with complex periodic potential”, Sb. Math., 208:10 (2017), 1535–1556  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    23. Tumanov S.N., Shkalikov A.A., “Eigenvalue Dynamics of a Pj -Symmetric Sturm-Liouville Operator and Criteria For Similarity to a Self-Adjoint Or a Normal Operator”, Dokl. Math., 96:3 (2017), 607–611  crossref  mathscinet  zmath  isi
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