1301.4196 (Jesús A. Álvarez López et al.)

Embedding theorems for the Dunkl harmonic oscillator    [PDF]

Jesús A. Álvarez López, Manuel Calaza

Embedding results of Sobolev type are proved for the Dunkl harmonic oscillator on the line. These results are generalized to operators on $\R_+$ of the form $P=-\frac{d^2}{dx^2}+sx^2-2f_1\frac{d}{dx}+f_2$, where $s>0$, and $f_1$ and $f_2$ are functions satisfying $f_2=\sigma(\sigma-1)x^{-2}-f_1^2-f_1'$ for some $\sigma>-1/2$.

View original: http://arxiv.org/abs/1301.4196