Open Access
November 2008 About spaces of $\omega_1$-$\omega_2$-ultradifferentiable functions
Jean Schmets, Manuel Valdivia
Bull. Belg. Math. Soc. Simon Stevin 15(4): 645-662 (November 2008). DOI: 10.36045/bbms/1225893945


Let $\Omega_1$ and $\Omega_2$ be non empty open subsets of $\mathbb R^r$ and $\mathbb R^s$ respectively and let $\omega_1$ and $\omega_2$ be weights. We introduce the spaces of ultradifferentiable functions $\mathcal{E}_{(\omega_1,\omega_2)}(\Omega_1 \times \Omega_2)$, $\mathcal{D}_{(\omega_1,\omega_2)}(\Omega_1 \times \Omega_2)$, $\mathcal{E}_{\{\omega_1,\omega_2\}}(\Omega_1 \times \Omega_2)$ and $\mathcal{D}_{\{\omega_1,\omega_2\}}(\Omega_1 \times \Omega_2)$, study their locally convex properties, examine the structure of their elements and also consider their links with the tensor products $\mathcal{E}_{*}(\Omega_1) \otimes \mathcal{E}_{*}(\Omega_2)$ and $\mathcal{D}_{*}(\Omega_1) \otimes \mathcal{D}_{*}(\Omega_2)$ endowed with the $\varepsilon$-, $\pi$- or $i$-topologies. This leads to kernel theorems.


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Jean Schmets. Manuel Valdivia. "About spaces of $\omega_1$-$\omega_2$-ultradifferentiable functions." Bull. Belg. Math. Soc. Simon Stevin 15 (4) 645 - 662, November 2008.


Published: November 2008
First available in Project Euclid: 5 November 2008

zbMATH: 1190.46025
MathSciNet: MR2475489
Digital Object Identifier: 10.36045/bbms/1225893945

Primary: 46A11 , 46A32 , 46E10 , 46F05

Keywords: Beurling type , kernel theorem , nuclearity , Roumieu type , tensor product , ultradifferentiable functions

Rights: Copyright © 2008 The Belgian Mathematical Society

Vol.15 • No. 4 • November 2008
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