publication . Other literature type . Article . 2008

About spaces of $\omega_1$-$\omega_2$-ultradifferentiable functions

Jean Schmets; Manuel Valdivia;
Open Access English
  • Published: 01 May 2008
  • Publisher: The Belgian Mathematical Society
Abstract
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 $\ma...
Subjects
arXiv: Mathematics::LogicMathematics::General TopologyPhysics::Chemical Physics
free text keywords: ultradifferentiable functions, Beurling type, Roumieu type, nuclearity, tensor product, kernel theorem, 46A11, 46A32, 46E10, 46F05, General Mathematics, Topology, Mathematical analysis, Mathematics
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publication . Other literature type . Article . 2008

About spaces of $\omega_1$-$\omega_2$-ultradifferentiable functions

Jean Schmets; Manuel Valdivia;