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arXiv · 2004.08727

Intertwining operator associated to symmetric groups and summability on the unit sphere

Yuan Xu
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Abstract

An integral representation of the intertwining operator for the Dunkl operators associated with symmetric groups is derived for the class of functions of a single component. The expression provides a closed form formula for the reproducing kernels of $h$-harmonics associated with symmetric groups when one of the components is a coordinate vector. The latter allows us to establish a sharp result for the Ces\`aro summability of $h$-harmonic series on the unit sphere.

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Yuan Xu. 2020-04-18. Intertwining operator associated to symmetric groups and summability on the unit sphere. https://arxiv.org/abs/2004.08727

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