dorsal/arxiv
View SchemaBiorthogonal polynomials associated with reflection groups and a formula of Macdonald
| Authors | Margit Rösler, Michael Voit |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9711004 |
| URL | https://arxiv.org/abs/q-alg/9711004 |
Abstract
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.
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"abstract": "Dunkl operators are differential-difference operators on $\\b R^N$ which\ngeneralize partial derivatives. They lead to generalizations of Laplace\noperators, Fourier transforms, heat semigroups, Hermite polynomials, and so on.\nIn this paper we introduce two systems of biorthogonal polynomials with respect\nto Dunkl\u0027s Gaussian distributions in a quite canonical way. These systems,\ncalled Appell systems, admit many properties known from classical Hermite\npolynomials, and turn out to be useful for the analysis of Dunkl\u0027s Gaussian\ndistributions. In particular, these polynomials lead to a new proof of a\ngeneralized formula of Macdonald due to Dunkl.\n The ideas for this paper are taken from recent works on non-Gaussian white\nnoise analysis and from the umbral calculus.",
"arxiv_id": "q-alg/9711004",
"authors": [
"Margit R\u00f6sler",
"Michael Voit"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Biorthogonal polynomials associated with reflection groups and a formula of Macdonald",
"url": "https://arxiv.org/abs/q-alg/9711004"
},
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