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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
MathSciNet review:
2120249
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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  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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Additional Information:
Florence
Scalas
Affiliation:
Université de Provence, LATP U.M.R. C.N.R.S. 6632, C.M.I., 39, rue F. Joliot Curie, 13453 Marseille cedex 13, France
Email:
scalas@cmi.univ-mrs.fr
DOI:
10.1090/S0002-9939-04-07703-2
PII:
S 0002-9939(04)07703-2
Received by editor(s):
October 21, 2003
Received by editor(s) in revised form:
February 5, 2004
Posted:
December 6, 2004
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2004,
American Mathematical Society
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