On Segal–Bargmann analysis for finite Coxeter groups and its heat kernel. (English) Zbl 1231.33016
Three versions of the Segal-Bargmann transform associated with finite reflection groups and rational Dunkl operators are presented in this paper. Some results obtained in this setting by S. Ben Saïd and B. Ørsted in [Math. Ann. 334, No. 2, 281–323 (2006; Zbl 1109.33015)] and F. Soltani in [Pac. J. Math. 214, No. 2, 379–397 (2004; Zbl 1052.33014)] are extended.
Reviewer: Luc Deleaval (Paris)
MSC:
| 33C52 | Orthogonal polynomials and functions associated with root systems |
| 45H05 | Integral equations with miscellaneous special kernels |
| 46E15 | Banach spaces of continuous, differentiable or analytic functions |
| 81S99 | General quantum mechanics and problems of quantization |
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