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

作者：Juan Huguet Jordi^*

来源：Integral Equations and Operator Theory, 2010, 68(2): 263-286.

DOI：10.1007/s00020-010-1816-5

• Hypoelliptic polynomial
• elliptic differential operator
• non-quasianalytic classes
• iterates of an operator

Let P be a linear partial differential operator with constant coefficients. For a weight function omega and an open subset Omega of R(N), the class epsilon(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 omega 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 epsilon(P,(omega))(Omega).

• 出版日期2010-10