Highly localized summability kernels on the sphere induced by Newtonian kernels

The purpose of this article is to construct highly localized summability kernels on the unit sphere in Rd that are restrictions to the sphere of linear combinations of a small number of shifts of the fundamental solution of the Laplace equation (Newtonian kernel) with poles outside the unit ball. The same problem is also solved for the subspace R(d-1 )in R-d.