Biorthogonal polynomials associated with reflection groups and a formula of Macdonald

Details Biorthogonal polynomials associated with reflection groups and a formula of Macdonald Biorthogonal polynomials associated with reflection groups and a formula of Macdonald

1997-11-03

arxiv.org/abs/q-alg/9711004v1

Mathematics

Quantum Algebra

14 pages, Latex2e

Scientific paper

Dunkl operators are differential-difference operators on $\b R^N$ which generalize partial derivatives. They lead to generalizations of Laplace operators, Fourier transforms, heat semigroups, Hermite polynomials, and so on. In this paper we introduce two systems of biorthogonal polynomials with respect to Dunkl's Gaussian distributions in a quite canonical way. These systems, called Appell systems, admit many properties known from classical Hermite polynomials, and turn out to be useful for the analysis of Dunkl's Gaussian distributions. In particular, these polynomials lead to a new proof of a generalized formula of Macdonald due to Dunkl. The ideas for this paper are taken from recent works on non-Gaussian white noise analysis and from the umbral calculus.

Affiliated with

Also associated with

No associations

Rating

Biorthogonal polynomials associated with reflection groups and a formula of Macdonald does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Biorthogonal polynomials associated with reflection groups and a formula of Macdonald, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Biorthogonal polynomials associated with reflection groups and a formula of Macdonald will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-62276