Geodesic
Composition in ultradifferentiable classes
Armin Rainer 1   ; Gerhard Schindl 1
1 Fakultät für Mathematik Universität Wien Oskar-Morgenstern-Platz 1 A-1090 Wien, Austria
Studia Mathematica, Tome 224 (2014) no. 2, pp. 97-131 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm224-2-1
Keywords: characterize stability under composition ultradifferentiable classes defined weight sequences weight functions omega generally weight matrices mathfrak investigate continuity composition mapsto circ addition represent beurling space mathcal omega roumieu space mathcal omega intersection union spaces mathcal mathcal associated weight sequences respectively

Armin Rainer  1   ; Gerhard Schindl  1

1 Fakultät für Mathematik Universität Wien Oskar-Morgenstern-Platz 1 A-1090 Wien, Austria 
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Armin Rainer; Gerhard Schindl. Composition in ultradifferentiable classes. Studia Mathematica, Tome 224 (2014) no. 2, pp. 97-131. doi: 10.4064/sm224-2-1

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