On balanced products of the distributions $x_{\pm}^{a}$ in Colombeau algebra $\EuScript{G}(\mathbb{R})$

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63584Results on products of the distributions $x_{\pm}^{a}$ and $\de^{(p)}(x)$ with coinciding singularities are derived when the products are balanced so that they exist in the distribution space. These results follow the idea of a known result on distributional products published by Jan Mikusiński in 1966. They are obtained in Colombeau algebra $\EuScript{G}(\mathbb{R})$ of generalized functions that contains the distribution space and the notion of 'association' in it allows obtaining results in terms of distributions.14 pagesFunctional Analysis46F30; 46F10On balanced products of the distributions $x_{\pm}^{a}$ in Colombeau algebra $\EuScript{G}(\mathbb{R})$text