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## Polynomial ultradistributions: differentiation and Laplace transformation

### Volume 88 / 2010

Banach Center Publications 88 (2010), 195-209 MSC: Primary 46F25; Secondary 46F12, 46G25. DOI: 10.4064/bc88-0-16

#### Abstract

We consider the multiplicative algebra $\mathsf P(\mathcal G_+')$ of continuous scalar polynomials on the space $\mathcal G_+'$ of Roumieu ultradistributions on $[0,\infty)$ as well as its strong dual $\mathsf P'(\mathcal G_+')$. The algebra $\mathsf P(\mathcal G_+')$ is densely embedded into $\mathsf P'(\mathcal G_+')$ and the operation of multiplication possesses a unique extension to $\mathsf P'(\mathcal G_+')$, that is, $\mathsf P'(\mathcal G_+')$ 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.

#### Authors

• O. ŁopuszańskiInstitute of Mathematics
University of Rzeszów
Rejtana 16A
35-310 Rzeszów, Poland
e-mail

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