The product of \(r^{-k}\) and \(\nabla\delta\) on \(\mathbb{R}^m\) (Q1590843)

From author's abstract: In the theory of distributions, there is a general lack of definitions for products and powers of distributions. The object of this paper is to apply Pizetti's formula and the normalization procedure to derive the product of \(r^{-k}\) and \(\nabla\delta\) (\(\nabla\) is the gradient operator) on \(\mathbb{R}^n\). The nice properties of the \(\delta\)-sequence are fully shown and used in the proof of our theorem.