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

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

2002-03-17

arxiv.org/abs/math/0203166v1

Mathematics

Functional Analysis

14 pages

Scientific paper

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.

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