Geodesic
A Bochner Theorem for Dunkl Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2011_7_a19,
     author = {Luc Vinet and Alexei Zhedanov},
     title = {A~Bochner {Theorem} for {Dunkl} {Polynomials}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2011},
     volume = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a19/}
}
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Luc Vinet; Alexei Zhedanov. A Bochner Theorem for Dunkl Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a19/

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