Letters in Mathematical Physics

, Volume 63, Issue 3, pp 219–228 | Cite as

Rank-One Singular Perturbations with a Dual Pair of Eigenvalues

  • Sergio Albeverio
  • Mykola Dudkin
  • Volodymyr Koshmanenko


We discuss the eigen-values problem for rank one singular perturbations \(\tilde A = A\tilde + \alpha \langle \cdot ,\omega \rangle \omega \) of a self-adjoint unbounded operator A with a gap in its spectrum. We give a constructive description of operators à which possess at least two new eigenvalues, one in the resolvent set and other in the spectrum of A.

eigen-value problem Krein's formula rank one singular perturbation self-adjoint extension 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Sergio Albeverio
    • 1
    • 2
    • 3
    • 4
  • Mykola Dudkin
    • 5
  • Volodymyr Koshmanenko
    • 6
  1. 1.Institut für Angewandte MathematikUniversität BonnBonnGermany
  2. 2.Bielefeld, Bonn, Germany
  3. 3.IZKSBonnGermany
  4. 4.CERFIM, Locarno and Acc. Arch. (USI)Switzerland
  5. 5.National Technical Uni.KyivUkraine
  6. 6.Institute of MathematicsKyivUkraine

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