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 g → f ◦ g.
Cite this article
Carmen Fernández, Antonio Galbis, Superposition in Classes of Ultradifferentiable Functions. Publ. Res. Inst. Math. Sci. 42 (2006), no. 2, pp. 399–419DOI 10.2977/PRIMS/1166642109