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 $mathcal E_omega^Psubseteqmathcal E_sigma^Q$. As a consequence we have a generalization of the classical Theorem of the Iterates.
Iterates of systems of operators in spaces of ω-ultradifferentiable functions
BOITI, Chiara
Primo
;
2016
Abstract
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 $mathcal E_omega^Psubseteqmathcal E_sigma^Q$. As a consequence we have a generalization of the classical Theorem of the Iterates.File in questo prodotto:
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