Abstract:
In this talk we explore the best approximation on the ball by means of
orthogonal polynomials associated with weight functions that are
invariant under reflection groups. A theory of orthogonal polynomials in
this context can be developed in analogy to that for the orthogonal
polynomials associated with standard spherical harmonics. Here, the
standard first order partial differential operators are replaced by a
family of commuting first order difference-differential operators: the
so called Dunkl operators.
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