A convolution product of (2j)th derivative of Dirac's delta in r and multiplicative distributional product between r−k and ∇(△jδ)

Abstract

The purpose of this paper is to obtain a relation between the distribution δ(2j)(r) and the operator △jδ and to give a sense to the convolution distributional product δ(2j)(r)∗δ(2s)(r) and the multiplicative distributional products r−k⋅∇(△jδ) and (r−c)−k⋅∇(△jδ).