A+ CATEGORY SCIENTIFIC UNIT

Composition in ultradifferentiable classes

Volume 224 / 2014

Armin Rainer, Gerhard Schindl 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.

Authors

  • Armin RainerFakultät für Mathematik
    Universität Wien
    Oskar-Morgenstern-Platz 1
    A-1090 Wien, Austria
    e-mail
  • Gerhard SchindlFakultät für Mathematik
    Universität Wien
    Oskar-Morgenstern-Platz 1
    A-1090 Wien, Austria
    e-mail

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