JournalsprimsVol. 42 , No. 2DOI 10.2977/prims/1166642109

Superposition in Classes of Ultradifferentiable Functions

  • Carmen Fernández

    Universitat de Valencia, Burjassot (Valencia), Spain
  • Antonio Galbis

    Universitat de Valencia, Burjassot (Valencia), Spain
Superposition in Classes of Ultradifferentiable Functions cover

Abstract

We present a complete characterization of the classes of ultradifferentiable functions that are holomorphically closed. Moreover, we show that any class holomorphically closed is also closed under composition (now without restrictions on the number of variables). In this case, we also discuss continuity and differentiability properties of the non-linear superposition operator gfg.