Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2001-09-30
Some Distributional Products of Mikusiński Type in the Colombeau Algebra $\mathcal G(R^m)$B. Damyanov (1) Bulgarian Academy of Sciences, Sofia, Bulgaria
Particular products of Schwartz distributions on the Euclidean space $\mathbb R^m$ are derived when the latter have coinciding point singularities and the products are ’balanced’ so that their sum to give an ordinary distribution. These products follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in the Colombeau algebra $\mathcal G (\mathbb R^m)$ of generalized functions. $\mathcal G (\mathbb R^m)$ is a relevant algebraic construction, with the distribution space linearly embedded, which by the notion of ’association’ allows the results to be evaluated on the level of distributions.
Keywords: Schwartz distributions, Colombeau generalized functions, multiplication of distributions
Damyanov B.: Some Distributional Products of Mikusiński Type in the Colombeau Algebra $\mathcal G(R^m)$. Z. Anal. Anwend. 20 (2001), 777-785. doi: 10.4171/ZAA/1045