International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 13, Pages 789-799
doi:10.1155/S0161171203110289
A convolution product of (2j)th derivative of Dirac's delta in r and multiplicative distributional product between
r−k and ∇(△jδ)
Núcleo Consolidado Matemática Pura y Aplicada (NUCOMPA), Facultad de Ciencias Exactas, UNCentro, Pinto 399, Tandil, Provincia de Buenos Aires (7000), Argentina
Received 29 October 2002
Copyright © 2003 Manuel A. Aguirre Téllez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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).