On the product of distributions in Colombeau algebra

Abstract: Results on singular products of Schwartz distributions on the Euclidean space R m 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: Schwartz distributions, multiplication, Colombeau generalized functions * The Schwartz distributions are widely employed in natural sciences and many other mathematical fields. Since products of distributions with coinciding singularities often appear in them, the problem of their multiplication has been objective of studies for a long time. On the other hand, the differential algebra G of generalized functions of J.F. Colombeau [1] has become popular since it has almost optimal properties for tackling non-linear problems of Schwartz distributions: they are linearly embedded in G and the multiplication is compatible with differentiation and products with smooth functions. The so-called 'association' in G, being a faithful generalization of the equality of distributions