Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (304 kB) Citations (21)
References:
PDF
HTML
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
\Bibitem{VinZhe11}
\by Luc Vinet, Alexei Zhedanov
\paper A~Bochner Theorem for Dunkl Polynomials
\jour SIGMA
\yr 2011
\vol 7
\papernumber 020
\totalpages 9
\mathnet{http://mi.mathnet.ru/sigma578}
\crossref{https://doi.org/10.3842/SIGMA.2011.020}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2804576}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000287879000004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855225269}
Linking options:
  • https://www.mathnet.ru/eng/sigma578
  • https://www.mathnet.ru/eng/sigma/v7/p20
    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:463
    Full-text PDF :103
    References:58
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024