02-147 B.P.Damyanov

ON BALANCED PRODUCTS OF THE DISTRIBUTIONS $x_{\pm}^{a}$ IN COLOMBEAU ALGEBRA (37K, Latex2e) Mar 25, 02

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Abstract. 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 of generalized functions, which contains the distribution space and the notion of 'association' in it allows obtaining results in terms of distributions.

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