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

Volume 118 / 2016

Chiara Boiti, Rachid Chaïli, Tayeb Mahrouz 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.

Authors

  • Chiara BoitiDipartimento di Matematica e Informatica
    Università di Ferrara
    Via Machiavelli 30
    I-44121 Ferrara, Italy
    e-mail
  • Rachid ChaïliUniversity of Sciences
    and Technology of Oran
    Oran, Algeria
    e-mail
    e-mail
  • Tayeb MahrouzUniversity Ibn Khaldoun of Tiaret
    Tiaret, Algeria
    e-mail

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