Imaginary Powers of the Dunkl Harmonic Oscillator - Nowak, A.; Stempak, K. (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
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 Z₂d. We prove that imaginary powers of this operator are bounded on Lp, 1 < p < ∞, and from L¹ into weak L¹.