Highly localized kernels on the sphere induced by Newtonian kernels

2018/08/26 by Kamen G. Ivanov, Ivanov, Kamen, Pencho Petrushev +1
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1808.08637

Abstract

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.

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