The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (211 KB) | Metadata | Table of Contents | ZAA summary
Volume 20, Issue 3, 2001, pp. 777–785
DOI: 10.4171/ZAA/1045

Published online: 2001-09-30

Some Distributional Products of Mikusiński Type in the Colombeau Algebra $\mathcal G(R^m)$

B. Damyanov[1]

(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