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Balanced Colombeau products of the distributions \(x_{\pm }^{-p}\) and \(x^{-p}\). (English) Zbl 1081.46027
Summary: 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 J. Mikusiński in [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 14, 511–513 (1966; Zbl 0163.36404)]. 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.

46F10 Operations with distributions and generalized functions
46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
Full Text: DOI arXiv EuDML
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