This article is cited in 6 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.

UDC: 517.984

Received: 21.11.2006

 English version: Siberian Mathematical Journal, 2008, 49:6, 968–984

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