ON BALANCED PRODUCTS OF
DISTRIBUTIONS IN COLOMBEAU ALGEBRA
Blagovest P. Damyanov
Institute for Nuclear Researches and Nuclear Energy
Bulgarian Academy of Sciences
72, Bul. Tzarigradsko Shosse, Sofia, 1784, BULGARIA
Abstract. Results on singular products of Schwartz distributions on the Euclidean space are derived when the products are so 'balanced' that they exist in the distribution space. The results follow the idea of a known distributional product introduced by Jan Mikusiński and are obtained in the Colombeau algebra of generalized functions. This algebra contains the distributions and the notion of 'association' permits obtaining results on the level of distributions.
AMS Subject Classification: 46F30, 46F10
Key Words and Phrases: Schwartz distributions, multiplication, Colombeau generalized functions


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DOI: 10.12732/ijam.v29i1.12

Volume: 29
Issue: 1
Year: 2016