ITERATES OF SYSTEMS OF OPERATORS IN SPACES OF ω-ULTRADIFFERENTIABLE FUNCTIONS

Given two systems $P = (Pj (D))_{j=1}^N$ and $Q = (Qj(D))_{j=1}^M$ 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