Certain incompatibilities are proved related to the prolongation of an associative derivation convolution algebra, defined for a subset of distributions, to a larger subset of distributions containing a derivation and the one distribution. This result is a twin of Schwartz’ impossibility theorem, stating certain incompatibilities related to the prolongation of the multiplication product from the set of continuous functions to a larger subset of distributions containing a derivation and the delta distribution. The presented result shows that the non-associativity of a recently constructed derivation convolution algebra of associated homogeneous distributions with support in R cannot be avoided.
@article{1311,
title = {On the impossibility of the convolution of distributions},
journal = {CUBO, A Mathematical Journal},
volume = {15},
year = {2013},
language = {en},
url = {http://dml.mathdoc.fr/item/1311}
}
Franssens, Ghislain R. On the impossibility of the convolution of distributions. CUBO, A Mathematical Journal, Tome 15 (2013) . http://gdmltest.u-ga.fr/item/1311/