Given $p \in \mathbb{N}$, a non empty open subset $\Omega$ of $\mathbb{R}^k$ and a semi-regular matrix $\mathfrak{M}$, we characterize the elements of the duals of the Beurling classes
$\mathcal{D}{(\mathfrak{M})}{\Omega}$ and $\\mathcal{D}_{L_p}{(\mathfrak{M})}{\Omega}$
of ultradifferentiable functions. We provide a global representation of these ultradistributions
with and without compact support by means of series involving measures in the first case
and elements of $\L_{loc}^{q}{\Omega}$ in the second.
Publié le : 2011-03-15
Classification:
countable intersection,
non quasi-analytic class,
ultradifferentiable function,
ultradistribution,
ultradistribution,
46F05,
46F20
@article{1301497747,
author = {Schmets, Jean and Valdivia, Manuel},
title = {Global structure of some ultradistributions},
journal = {Funct. Approx. Comment. Math.},
volume = {44},
number = {1},
year = {2011},
pages = { 63-78},
language = {en},
url = {http://dml.mathdoc.fr/item/1301497747}
}
Schmets, Jean; Valdivia, Manuel. Global structure of some ultradistributions. Funct. Approx. Comment. Math., Tome 44 (2011) no. 1, pp. 63-78. http://gdmltest.u-ga.fr/item/1301497747/