Abstract
Let P be a linear partial differential operator with constant coefficients. For a weight function ω and an open subset Ω of \({\mathbb{R}^N}\) , the class \({\mathcal{E}_{P,\{\omega\}}(\Omega)}\) 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 \({\mathcal{E}_{P,(\omega)}(\Omega)}\).
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Jordi Juan-Huguet was partially supported by MEC and FEDER Project MTM2007-62643, Conselleria d’Educació de la GVA, Project GV/2010/040, grant F.P.U. AP-2006-04678 and the research net MTM2007-30904-E.
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Juan-Huguet, J. Iterates and Hypoellipticity of Partial Differential Operators on Non-Quasianalytic Classes. Integr. Equ. Oper. Theory 68, 263–286 (2010). https://doi.org/10.1007/s00020-010-1816-5
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DOI: https://doi.org/10.1007/s00020-010-1816-5