Results on Singular Distribution Products of Mikusiński Type

Results on products of Schwartz distributions are obtained when they have coinciding point singularities and only sums of the products exist in the distribution space. These results follow the pattern of a well-know distributional product published by Jan Mikusiński in 1966, and are named Mikusiński type products. The formulas are derived as the distributions are embedded in Colombeau algebra of generalized functions. This algebra possesses optimal properties regarding the distributional multiplication, and its notion of “association” allows one to obtain the results in terms of distributions.