Results 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 Mikusi\'nski 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.
Categories: math.FA