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Poisson integrals associated to Dunkl operators for dihedral groups

Author(s): Florence Scalas
Journal: Proc. Amer. Math. Soc. 133 (2005), 1713-1720.
MSC (2000): Primary 30E25, 31A10, 31A20; Secondary 31A05
Posted: December 6, 2004
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Abstract: In this paper we study the boundary behavior of Poisson integrals associated to Dunkl differential-difference operators for dihedral groups and the boundary integral representations for functions on the unit disc of $\mathbb{C}$ annihilated by the Laplace operator corresponding to these differential-difference operators.

References:

[D1]: C. F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989), 167-183. MR 0951883 (90k:33027)
[D2]: C. F. Dunkl, Poisson and Cauchy kernels for orthogonal polynomials with dihedral symmetry, J. Math. Anal. Appl. 143 (1989), 459-470. MR 1022547 (91a:42021)
[DX]: C. F. Dunkl and Y. Xu, Orthogonal polynomials of several variables, Cambridge University Press, 2001. MR 1827871 (2002m:33001)
[R]: M. Rösler, Generalized Hermite polynomials and the heat equation for Dunkl operators, Comm. Math. Phys. 192 (1998), 519-542. MR 1620515 (99k:33048)


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