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Spectral asymptotics for nonsmooth perturbations of the harmonic oscillator

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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.

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Authors and Affiliations

  1. Socio-Economics Research Institute, Ufa, Russia

    E. F. Akhmerova

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  1. E. F. Akhmerova
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Correspondence to E. F. Akhmerova.

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Original Russian Text Copyright © 2008 Akhmerova E. F.

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Ufa. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1216–1234, November–December, 2008.

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Akhmerova, E.F. Spectral asymptotics for nonsmooth perturbations of the harmonic oscillator. Sib Math J 49, 968–984 (2008). https://doi.org/10.1007/s11202-008-0093-x

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  • DOI: https://doi.org/10.1007/s11202-008-0093-x

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