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 , 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.
