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

2020/04/18 by Xu, Yuan
#33C52 #42C05. Secondary 42B08 #44A30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.08727

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 Cesàro summability of h-harmonic series on the unit sphere.

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