On spectral asymptotics of nonselfadjoint Sturm-Liouville operator with a slowly growing potential

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Doklady Bashkirskogo Universiteta. 2016. Volume 1. No. 2. pp. 259-264.

Authors

Valiullina L. G.
Bashkir State University
32 Zaki Validi st., 450074 Ufa, Republic of Bashkortostan, Russia
Ishkin Kh. K.*
Bashkir State University
32 Zaki Validi st., 450074 Ufa, Republic of Bashkortostan, Russia

Abstract

The paper proposes a new approach that allows to study the problem of spectral asymptotics of nonselfadjoint differential operators. The approach is based on a modification of the method of M. Keldysh for the study of the conditions of spectral localization of relatively compact perturbations of selfadjoint operators with resolvent of a class of Neumann-Schatten. The conditions on the perturbation V , which preserve the asymptotic behavior of the spectrum of the operator - y'' + eiθ lnxy have been obtained.

Keywords

  • nonselfadjoint operators
  • Keldysh theorem
  • spectral instability
  • spectral localization
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