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Balanced Colombeau products of the distributions $x_{\pm}^{-p}$ and $x^{-p}$
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 189-201
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Results on singular products of the distributions $x_{\pm }^{-p}$ and $x^{-p}$ for natural $p$ are derived, when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.
Results on singular products of the distributions $x_{\pm }^{-p}$ and $x^{-p}$ for natural $p$ are derived, when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.
Classification : 46F10, 46F30
Keywords: Schwartz distributions; multiplication; Colombeau generalized functions 
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Damyanov, B. P. Balanced Colombeau products of the distributions  $x_{\pm}^{-p}$ and $x^{-p}$. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 189-201. http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a13/

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