## Highly Localized Kernels on the Sphere Induced by Newtonian kernels

**A 2017 Preprint by
K. Ivanov and
P. Petrushev
**

- 2017:02
The purpose of this article is to construct highly localized summability kernels on the unit sphere in ${\bf R}^d$ 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 ${\bf R}^d$. The same problem is also solved for the subspace ${\bf R}^{d-1}$ in ${\bf R}^d$.