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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 020, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.020 (Mi sigma578) 		 
This article is cited in 21 scientific papers (total in 21 papers)

A Bochner Theorem for Dunkl Polynomials

Luc Vineta, Alexei Zhedanovb

a Centre de recherches mathématiques Universite de Montréal, P.O. Box 6128, Centre-ville Station, Montréal (Québec), H3C 3J7 Canada
b Donetsk Institute for Physics and Technology, Donetsk 83114, Ukraine
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DOI: https://doi.org/10.3842/SIGMA.2011.020
Abstract: We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural conditions it is seen that the only families of orthogonal polynomials in this category are limits of little and big $q$-Jacobi polynomials as $q=-1$.
Keywords: classical orthogonal polynomials; Dunkl operators; Jacobi polynomials; little $q$-Jacobi polynomials; big $q$-Jacobi polynomials.
Received: November 30, 2010; in final form February 25, 2011; Published online February 27, 2011
Bibliographic databases:
Document Type: Article
MSC: 33C45; 33C47; 42C05
Language: English
Citation: Luc Vinet, Alexei Zhedanov, “A Bochner Theorem for Dunkl Polynomials”, SIGMA, 7 (2011), 020, 9 pp.
Citation in format AMSBIB
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\paper A~Bochner Theorem for Dunkl Polynomials
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    • This publication is cited in the following 21 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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