Iterates and Hypoellipticity of Partial Differential Operators on Non-Quasianalytic Classes |
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Authors: | Jordi Juan-Huguet |
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Affiliation: | 1. Instituto de Matemática Pura y Aplicada IUMPA, Universidad Politécnica de Valencia, 46071, Valencia, Spain
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Abstract: | Let P be a linear partial differential operator with constant coefficients. For a weight function ω and an open subset Ω of mathbbRN{mathbb{R}^N} , the class EP,{w}(W){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 EP,(w)(W){mathcal{E}_{P,(omega)}(Omega)}. |
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