JournalszaaVol. 20, No. 3pp. 777–785

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

  • B. Damyanov

    Bulgarian Academy of Sciences, Sofia, Bulgaria
Some Distributional Products of Mikusiński Type in the Colombeau Algebra $\mathcal G(R^m)$ cover
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Abstract

Particular products of Schwartz distributions on the Euclidean space Rm\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 G(Rm)\mathcal G (\mathbb R^m) of generalized functions. G(Rm)\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.

Cite this article

B. Damyanov, Some Distributional Products of Mikusiński Type in the Colombeau Algebra G(Rm)\mathcal G(R^m). Z. Anal. Anwend. 20 (2001), no. 3, pp. 777–785

DOI 10.4171/ZAA/1045