Imaginary Powers of the Dunkl Harmonic Oscillator

Details Imaginary Powers of the Dunkl Harmonic Oscillator Imaginary Powers of the Dunkl Harmonic Oscillator

2009-02-11

arxiv.org/abs/0902.1958v1

SIGMA 5 (2009), 016, 12 pages

Mathematics

Classical Analysis and ODEs

Scientific paper

10.3842/SIGMA.2009.016

In this paper we continue the study of spectral properties of the Dunkl
harmonic oscillator in the context of a finite reflection group on
$\mathbb{R}^d$ isomorphic to $\mathbb{Z}^d_2$. We prove that imaginary powers
of this operator are bounded on $L^p$, $1$L^1$.

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