A Bochner Theorem for Dunkl Polynomials

Details A Bochner Theorem for Dunkl Polynomials A Bochner Theorem for Dunkl Polynomials

2010-11-05

arxiv.org/abs/1011.1457v3

SIGMA 7 (2011), 020, 9 pages

Mathematics

Classical Analysis and ODEs

Scientific paper

10.3842/SIGMA.2011.020

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 $q=-1$.

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