A type of perturbation of the harmonic oscillator

Details A type of perturbation of the harmonic oscillator A type of perturbation of the harmonic oscillator

2011-01-26

arxiv.org/abs/1101.5022v5

Mathematics

Spectral Theory

Scientific paper

Eigenfunction estimates and embedding results are proved for the Dunkl
harmonic oscillator. These kind of 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 $\sigma>-1/2$.

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