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

[摘要] 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 Cesaro summability of h-harmonic series on the unit sphere. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Intertwining operator;Symmetric group;Dunkl operators;h-spherical harmonics;Summability