Results on Colombeau product of distributions
Damyanov, Blagovest
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 627-634 / Harvested from Czech Digital Mathematics Library
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The differential $\Bbb C$-algebra $\Cal G(\Bbb R^m)$ of generalized functions of J.-F. Colombeau contains the space $\Cal D'(\Bbb R^m)$ of Schwartz distributions as a $\Bbb C$-vector subspace and has a notion of `association' that is a faithful generalization of the weak equality in $\Cal D'(\Bbb R^m)$. This is particularly useful for evaluation of certain products of distributions, as they are embedded in $\Cal G(\Bbb R^m)$, in terms of distributions again. In this paper we propose some results of that kind for the products of the widely used distributions $x_{\pm}^a$ and $\delta ^{(p)}(x)$, with $x$ in $\Bbb R^m$, that have coinciding singular supports. These results, when restricted to dimension one, are also easily transformed into the setting of regularized model products in the classical distribution theory.

Publié le : 1997-01-01
Classification:  46F10 
@article{118961,
     author = {Blagovest Damyanov},
     title = {Results on Colombeau product of distributions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {627-634},
     zbl = {0937.46030},
     mrnumber = {1601668},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118961}
}

Damyanov, Blagovest. Results on Colombeau product of distributions. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 627-634. http://gdmltest.u-ga.fr/item/118961/

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