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Sibirsk. Mat. Zh., 2008, Volume 49, Number 6, Pages 1216–1234 (Mi smj1913)  

This article is cited in 4 scientific papers (total in 4 papers)

Spectral asymptotics for nonsmooth perturbations of the harmonic oscillator

È. F. Akhmerova

Institute of Social and Economic Researchs, Ufa Science Centre, Russian Academy of Sciences

Abstract: We obtain the spectral asymptotics of a nonsmooth perturbation of the one-dimensional harmonic oscillator. We use the technique of perturbation theory which is based on an asymptotic presentation of the part of the kernel of the nonperturbed operator resolvent in some neighborhood of an eigenvalue.

Keywords: harmonic oscillator, spectral asymptotics, nonsmooth perturbation.

Full text: PDF file (355 kB)
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English version:
Siberian Mathematical Journal, 2008, 49:6, 968–984

Bibliographic databases:

UDC: 517.984
Received: 21.11.2006

Citation: È. F. Akhmerova, “Spectral asymptotics for nonsmooth perturbations of the harmonic oscillator”, Sibirsk. Mat. Zh., 49:6 (2008), 1216–1234; Siberian Math. J., 49:6 (2008), 968–984

Citation in format AMSBIB
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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. È. F. Akhmerova, “Asymptotics of the Spectrum of Nonsmooth Perturbations of Differential Operators of Order $2m$”, Math. Notes, 90:6 (2011), 813–823  mathnet  crossref  crossref  mathscinet  isi
    2. E. F. Akhmerova, “Asimptoticheskie predstavleniya sobstvennykh funktsii dvumernogo garmonicheskogo ostsillyatora”, Ufimsk. matem. zhurn., 3:4 (2011), 14–20  mathnet  zmath
    3. Adduci J., Mityagin B., “Eigensystem of an L-2-perturbed harmonic oscillator is an unconditional basis”, Cent Eur J Math, 10:2 (2012), 569–589  crossref  mathscinet  zmath  isi  elib  scopus
    4. Adduci J., Mityagin B., “Root System of a Perturbation of a Selfadjoint Operator with Discrete Spectrum”, Integr. Equ. Oper. Theory, 73:2 (2012), 153–175  crossref  mathscinet  zmath  isi  elib  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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