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

Chiara Boiti¹ ; Rachid Chaïli² ; Tayeb Mahrouz³

¹ Dipartimento di Matematica e Informatica Università di Ferrara Via Machiavelli 30 I-44121 Ferrara, Italy
² University of Sciences and Technology of Oran Oran, Algeria
³ University Ibn Khaldoun of Tiaret Tiaret, Algeria

Annales Polonici Mathematici, Tome 118 (2016) no. 2-3, pp. 95-111.

Résumé

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.

Détail

DOI : 10.4064/ap4024-12-2016

Keywords: given systems linear partial differential operators constant coefficients consider spaces mathcal omega mathcal sigma weighted ultradifferentiable functions respect iterates systems respectively necessary sufficient conditions systems weights omega sigma inclusion mathcal omega subseteq mathcal sigma consequence obtain generalization classical theorem iterates