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.
@article{10_4064_sm224_2_1,
author = {Armin Rainer and Gerhard Schindl},
title = {Composition in ultradifferentiable classes},
journal = {Studia Mathematica},
pages = {97--131},
year = {2014},
volume = {224},
number = {2},
doi = {10.4064/sm224-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm224-2-1/}
}
TY - JOUR
AU - Armin Rainer
AU - Gerhard Schindl
TI - Composition in ultradifferentiable classes
JO - Studia Mathematica
PY - 2014
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EP - 131
VL - 224
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UR - http://geodesic.mathdoc.fr/articles/10.4064/sm224-2-1/
DO - 10.4064/sm224-2-1
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%J Studia Mathematica
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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
