Dunkl kernel associated with dihedral groups
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TL;DR: In this article, it was shown that the Dunkl intertwining operator can be computed on homogeneous polynomials when the root system is of dihedral type and under a mild assumption on the multiplicity function.
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About: This article is published in Journal of Mathematical Analysis and Applications. The article was published on 15 Dec 2015. and is currently open access. The article focuses on the topics: Dihedral group & Standard basis.
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Citations
The Dunkl kernel and intertwining operator for dihedral groups
Hendrik De Bie,Pan Lian +1 more
TL;DR: In this article, an integral expression for the Dunkl kernel, which is the integral kernel of the Fourier transform, for all dihedral groups was derived. But this result is not applicable to the case of finite reflection groups.
Two-step asymptotics of scaled Dunkl processes
Sergio Andraus,Seiji Miyashita +1 more
TL;DR: In this paper, the authors studied scaled Dunkl processes and derived expressions for the intertwining operator in order to calculate the asymptotics of the distribution function in two limiting situations.
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Intertwining Operators Associated with Dihedral Groups
TL;DR: In this paper, the authors derived closed formulas for poisson kernels of h-harmonics and sieved Gegenbauer polynomials when one of the variables is at vertices of a regular polygon.
10
Two-step asymptotics of scaled Dunkl processes
Sergio Andraus,Seiji Miyashita +1 more
TL;DR: In this article, the authors studied scaled Dunkl processes and derived expressions for the intertwining operator in order to calculate the asymptotics of the distribution function in two limiting situations.
8
Laplace-type integral representations of the generalized Bessel function and of the Dunkl kernel of type $B_2$
Béchir Amri,Nizar Demni +1 more
TL;DR: In this paper, a Laplace-type integral representation for generalized Bessel functions and the Dunkl kernel associated with the rank-two root system of type B_2 was derived.
8
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Orthogonal Polynomials of Several Variables
Charles F. Dunkl,Yuan Xu +1 more
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