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 Z_2^d. We prove that imaginary powers of this operator are bounded on L^p, 1 < p < ∞, and from L^1 into weak L^1.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2009-02-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.016 |
| 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 Z_2^d. We prove that imaginary powers of this operator are bounded on L^p, 1 < p < ∞, and from L^1 into weak L^1. |
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| ISSN: | 1815-0659 |