Iterates of systems of operators in spaces of $\omega$-ultradifferentiable functions

Abstract

Given two systems $P=(P_j(D){)}_{j=1}^N$ and $Q=(Q_j(D){)}_{j=1}^M$ of linear partial differential operators with constant coefficients, we consider the spaces ${\mathcal{E}}_{\omega }^P$ and ${\mathcal{E}}_{\omega }^Q$ of $\omega$-ultradifferentiable functions with respect to the iterates of the systems $P$ and $Q$ respectively. We find necessary and sufficient conditions, on the systems and on the weights $\omega (t)$ and $\sigma (t)$, for the inclusion ${\mathcal{E}}_{\omega }^P\subseteq {\mathcal{E}}_{\sigma }^Q$. As a consequence we have a generalization of the classical Theorem of the Iterates.

Cited by in corpus (1)

• The Theorem of Iterates for elliptic and non-elliptic Operators