  The purpose of this article is to construct highly localized summability
kernels on the unit sphere in ${\mathbb R}^d$ 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 in ${\mathbb R}^d$. The same problem is also solved for the subspace
${\mathbb R}^{d-1}$ in ${\mathbb R}^d$.
