Imaginary Powers of the Dunkl Harmonic Oscillator

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.

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Bibliographic Details
Published in:	Symmetry, integrability and geometry, methods and applications Vol. 5; p. 016
Main Author:	Nowak, Adam
Format:	Journal Article
Language:	English
Published:	Kiev National Academy of Sciences of Ukraine 01-01-2009 National Academy of Science of Ukraine
Subjects:	Calderón-Zygmund operators Dunkl harmonic oscillator Dunkl operators imaginary powers
Online Access:	Get full text
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Description
Summary:	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.
ISSN:	1815-0659 1815-0659
DOI:	10.3842/SIGMA.2009.016