Intertwining operator associated to symmetric groups and summability on the unit sphere
Classical Analysis and ODEs
2020-04-21 v1
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 -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 -harmonic series on the unit sphere.
Cite
@article{arxiv.2004.08727,
title = {Intertwining operator associated to symmetric groups and summability on the unit sphere},
author = {Yuan Xu},
journal= {arXiv preprint arXiv:2004.08727},
year = {2020}
}