Iterates and Hypoellipticity of Partial Differential Operators on Non-Quasianalytic Classes

摘要

Let P be a linear partial differential operator with constant coefficients. For a weight function ω and an open subset Ω of ?~N, the class _(P,{ω})(ω) of Roumieu type involving the successive iterates of the operator P is considered. The completeness of this space is characterized in terms of the hypoellipticity of P. Results of Komatsu and Newberger-Zielezny are extended. Moreover, for weights ω satisfying a certain growth condition, this class coincides with a class of ultradifferentiable functions if and only if P is elliptic. These results remain true in the Beurling case P,_({ω})(ω).