Iterates of systems of operators in spaces of $\omega $-ultradifferentiable functions
Volume 118 / 2016
Annales Polonici Mathematici 118 (2016), 95-111
MSC: Primary 35E20; Secondary 46E10, 35H99.
DOI: 10.4064/ap4024-12-2016
Published online: 22 December 2016
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 ${\mathcal E}_\sigma ^Q$ of weighted-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 obtain a generalization of the classical Theorem of the Iterates.
