Composition in ultradifferentiable classes
Volume 224 / 2014
Studia Mathematica 224 (2014), 97-131
MSC: 26E10, 30D60, 46E10, 47B33.
DOI: 10.4064/sm224-2-1
Abstract
We characterize stability under composition of ultradifferentiable classes defined by weight sequences $M$, by weight functions $\omega $, and, more generally, by weight matrices $\mathfrak {M}$, and investigate continuity of composition $(g,f) \mapsto f \circ g$. In addition, we represent the Beurling space $\mathcal {E}^{(\omega )}$ and the Roumieu space $\mathcal {E}^{\{\omega \}}$ as intersection and union of spaces $\mathcal {E}^{(M)}$ and $\mathcal {E}^{\{M\}}$ for associated weight sequences, respectively.
