We consider the multiplicative algebra P(𝒢₊') of continuous scalar polynomials on the space 𝒢₊' of Roumieu ultradistributions on [0,∞) as well as its strong dual P'(𝒢₊'). The algebra P(𝒢₊') is densely embedded into P'(𝒢₊') and the operation of multiplication possesses a unique extension to P'(𝒢₊'), that is, P'(𝒢₊') is also an algebra. The operation of differentiation on these algebras is investigated. The polynomially extended Laplace transformation and its connections with the differentiation are also studied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-16,
author = {O. \L opusza\'nski},
title = {Polynomial ultradistributions: differentiation and Laplace transformation},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {195-209},
zbl = {1203.46028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-16}
}
O. Łopuszański. Polynomial ultradistributions: differentiation and Laplace transformation. Banach Center Publications, Tome 89 (2010) pp. 195-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-16/