Results on Colombeau product of distributions

Damyanov, Blagovest. "Results on Colombeau product of distributions." Commentationes Mathematicae Universitatis Carolinae 38.4 (1997): 627-634. <http://eudml.org/doc/248052>.

@article{Damyanov1997,
abstract = {The differential $\mathbb \{C\}$-algebra $\mathcal \{G\}(\mathbb \{R\}^m)$ of generalized functions of J.-F. Colombeau contains the space $\mathcal \{D\}^\{\prime \}(\mathbb \{R\}^m)$ of Schwartz distributions as a $\mathbb \{C\}$-vector subspace and has a notion of ‘association’ that is a faithful generalization of the weak equality in $\mathcal \{D\}^\{\prime \}(\mathbb \{R\}^m)$. This is particularly useful for evaluation of certain products of distributions, as they are embedded in $\mathcal \{G\}(\mathbb \{R\}^m)$, 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 $\mathbb \{R\}^m$, 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.},
author = {Damyanov, Blagovest},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {multiplication of Schwartz distributions; Colombeau generalized functions; multiplication of Schwartz distributions; Colombeau generalized functions},
language = {eng},
number = {4},
pages = {627-634},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Results on Colombeau product of distributions},
url = {http://eudml.org/doc/248052},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Damyanov, Blagovest
TI - Results on Colombeau product of distributions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 4
SP - 627
EP - 634
AB - The differential $\mathbb {C}$-algebra $\mathcal {G}(\mathbb {R}^m)$ of generalized functions of J.-F. Colombeau contains the space $\mathcal {D}^{\prime }(\mathbb {R}^m)$ of Schwartz distributions as a $\mathbb {C}$-vector subspace and has a notion of ‘association’ that is a faithful generalization of the weak equality in $\mathcal {D}^{\prime }(\mathbb {R}^m)$. This is particularly useful for evaluation of certain products of distributions, as they are embedded in $\mathcal {G}(\mathbb {R}^m)$, 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 $\mathbb {R}^m$, 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.
LA - eng
KW - multiplication of Schwartz distributions; Colombeau generalized functions; multiplication of Schwartz distributions; Colombeau generalized functions
UR - http://eudml.org/doc/248052
ER -