Biorthogonal polynomials associated with reflection groups and a formula of Macdonald

DOI10.1016/S0377-0427(98)00168-XzbMath0928.33012arXivq-alg/9711004MaRDI QIDQ1298577

Michael Voit, Margit Rösler

Publication date: 3 January 2000

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9711004

zbMATH Keywords

generalized Hermite polynomialsAppell systemsbiorthogonal polynomialsDunkl operators

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Other transforms and operators of Fourier type (43A32) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (5)

Positivity of Dunkl's intertwining operator ⋮ Generalized Fock spaces and Weyl relations for the Dunkl kernel on the real line ⋮ Inversion formulas in the Dunkl-type heat conduction on ⋮ Markov processes related with Dunkl operators ⋮ On a universality property of certain integral operators

Cites Work

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• The volume of a compact Lie group
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• Generalized Hermite polynomials and the heat equation for Dunkl operators
• Markov processes related with Dunkl operators
• The Dunkl transform
• Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement
• Non-Gaussian infinite dimensional analysis
• Nonsymmetric Jack polynomials and integral kernels
• Positivity of Dunkl's intertwining operator
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance

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