Imaginary Powers of the Dunkl Harmonic Oscillator

Abstract

Doi: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 Rd isomorphic to Zd 2. We prove that imaginary powers of this operator are bounded on Lp, 1 < p < ∞, and from L1 into weak L1