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arXiv · 0902.1958

Imaginary Powers of the Dunkl Harmonic Oscillator

Adam Nowak·Krzysztof Stempak
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Abstract

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 $L^p$, $1<p<\infty$, and from $L^1$ into weak $L^1$.

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Adam Nowak, Krzysztof Stempak. 2009-02-11. Imaginary Powers of the Dunkl Harmonic Oscillator. https://doi.org/10.3842/sigma.2009.016

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