Imaginary Powers of the Dunkl Harmonic Oscillator

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2009
• Hauptverfasser: Nowak, A., Stempak, K.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2009
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/149244
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Imaginary Powers of the Dunkl Harmonic Oscillator / A. Nowak, K. Stempak // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 15 назв. — англ.

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.