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TMF, 2007, Volume 151, Number 2, Pages 207–218 (Mi tmf6040)  

This article is cited in 8 scientific papers (total in 8 papers)

Some singular perturbations of periodic operators

D. I. Borisov

Bashkir State Pedagogical University

Abstract: We consider two examples of singular perturbations of a periodic differential operator on the axis. The first example is a rapidly oscillating potential with compact support, and the second example is the delta potential with a small complex coupling constant. We investigate the structure and asymptotic behavior of the spectrum of the perturbed operators in detail.

Keywords: perturbation, periodic operator, spectrum, asymptotic expansion

DOI: https://doi.org/10.4213/tmf6040

Full text: PDF file (407 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 151:2, 614–624

Bibliographic databases:

Received: 08.09.2006
Revised: 23.10.2006

Citation: D. I. Borisov, “Some singular perturbations of periodic operators”, TMF, 151:2 (2007), 207–218; Theoret. and Math. Phys., 151:2 (2007), 614–624

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v151/i2/p207

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

    This publication is cited in the following articles:
    1. D. I. Borisov, “Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S35–S45  mathnet  crossref  elib
    2. D. I. Borisov, “Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients”, St. Petersburg Math. J., 20:2 (2009), 175–191  mathnet  crossref  mathscinet  zmath  isi
    3. D. I. Borisov, “On the spectrum of a two-dimensional periodic operator with a small localized perturbation”, Izv. Math., 75:3 (2011), 471–505  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. Yu. Trynin, “On inverse nodal problem for Sturm-Liouville operator”, Ufa Math. J., 5:4 (2013), 112–124  mathnet  crossref  elib
    5. D.I. Borisov, R. Kh. Karimov, T. F. Sharapov, “Initial length scale estimate for waveguides with some random singular potentials”, Ufa Math. J., 7:2 (2015), 33–54  mathnet  crossref  isi  elib
    6. Drouot A., “Bound States For Rapidly Oscillatory Schrodinger Operators in Dimension 2”, SIAM J. Math. Anal., 50:2 (2018), 1471–1484  crossref  mathscinet  zmath  isi  scopus
    7. Drouot A., “Resonances For Random Highly Oscillatory Potentials”, J. Math. Phys., 59:10 (2018), 101506  crossref  mathscinet  zmath  isi  scopus
    8. Drouot A., “Scattering Resonances For Highly Oscillatory Potentials”, Ann. Sci. Ec. Norm. Super., 51:4 (2018), 865–925  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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