# 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

## Abstract

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 language English 147-167 21 Letters in Mathematical Physics 106 2 https://doi.org/10.1007/s11005-015-0805-7 Published - 1 Feb 2016 Yes

## Keywords

• harmonic oscillator