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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 016, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.016 (Mi sigma362) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Imaginary Powers of the Dunkl Harmonic Oscillator

Adam Nowak, Krzysztof Stempak

Instytut Matematyki i Informatyki, Politechnika Wroclawska, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland
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DOI: https://doi.org/10.3842/SIGMA.2009.016
Abstract: In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on $\mathbb R^d$ isomorphic to $\mathbb Z^d_2$. We prove that imaginary powers of this operator are bounded on $L^p$, $1<p<\infty$, and from $L^1$ into weak $L^1$.
Keywords: Dunkl operators; Dunkl harmonic oscillator; imaginary powers; Calderón–Zygmund operators.
Received: October 14, 2008; in final form February 8, 2009; Published online February 11, 2009
Bibliographic databases:
Document Type: Article
MSC: 42C10; 42C20
Language: English
Citation: Adam Nowak, Krzysztof Stempak, “Imaginary Powers of the Dunkl Harmonic Oscillator”, SIGMA, 5 (2009), 016, 12 pp.
Citation in format AMSBIB
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\by Adam Nowak, Krzysztof Stempak
\paper Imaginary Powers of the Dunkl Harmonic Oscillator
\jour SIGMA
\yr 2009
\vol 5
\papernumber 016
\totalpages 12
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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