Root System of Singular Perturbations of the Harmonic Oscillator Type Operators

Boris Mityagin, Petr Siegl*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We analyze perturbations of the harmonic oscillator type operators in a Hilbert space $${\mathcal{H}}$$H, i.e. of the self-adjoint operator with simple positive eigenvalues μk satisfying μk+1 − μk ≥ 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.

Original languageEnglish
Pages (from-to)147-167
Number of pages21
JournalLetters in Mathematical Physics
Issue number2
Publication statusPublished - 1 Feb 2016
Externally publishedYes


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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