Balanced Colombeau products of the distributions x_±^-p and x^-p

2002/03/24 by B. P. Damyanov, Blagovest Damyanov, Damyanov, B. P.
Mathematics · #46F10 #46F30 #FOS: Mathematics #Functional Analysis (math.FA) #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Probability and Statistical Research #math.FA #msc:46F10 #msc:46F30

paper · pdf · doi:10.48550/arxiv.math/0203251

11 pages

arxiv created 2002/03/24 · openalex publication_date 2002/03/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Results on singular products of the distributions x_±^-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 Colombeau algebra of generalized functions, which is most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.

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