A Perturbation of the Dunkl Harmonic Oscillator on the Line

Jesús A. Álvarez López, Manuel Calaza, Carlos Franco

Let $J_{\sigma }$ be the Dunkl harmonic oscillator on $\mathbb{R}$ ($\sigma >-\frac{1}{2}$). For $0<u<1$ and $\xi >0$, it is proved that, if $\sigma >u-\frac{1}{2}$, then the operator $U=J_σ+ξ|x|^{-2u}…