The surjectivity of a constant coefficient homogeneous differential operator in the real analytic functions and the geometry of its symbol

Braun, Rüdiger W.

Annales de l'Institut Fourier, Tome 45 (1995) no. 1, pp. 223-249.

Hörmander a caractérisé les opérateurs différentiels à coefficients constants sur l’espace des fonctions analytiques réelles sur ${ℝ}^N$ par une condition du type Phragmén-Lindelöf. On donne des conséquences géométriques de cette condition et, pour les opérateurs homogènes, de la condition analogue pour les classes de Gevrey.

Hörmander has characterized the surjective constant coefficient partial differential operators on the space of all real analytic functions on ${ℝ}^N$ by a Phragmén-Lindelöf condition. Geometric implications of this condition and, for homogeneous operators, of the corresponding condition for Gevrey classes are given.

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