Letters in Mathematical Physics

, Volume 106, Issue 2, pp 147–167 | Cite as

Root System of Singular Perturbations of the Harmonic Oscillator Type Operators

Article

Abstract

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space \({\mathcal{H}}\), i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Keywords

non-self-adjoint operators harmonic oscillator Riesz basis quadratic forms singular potentials 

Mathematics Subject Classification

47A55 47A70 34L10 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Mathematishes InstitutUniversität BernBernSwitzerland
  3. 3.Nuclear Physics Institute ASCRŘežCzech Republic

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