A New Proof of Okaji’s Theorem  for a Class of Sum of Squares Operators

Cordaro, Paulo D.; Hanges, Nicholas

A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators
[Une Nouvelle Preuve du Théorème d’Okaji pour une Classe d’Opérateurs “Somme de Carrés”]

Cordaro, Paulo D. ; Hanges, Nicholas

Annales de l'Institut Fourier, Tome 59 (2009), p. 595-619 / Harvested from Numdam

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Résumé
Abstract

Soit $P$ un opérateur différentiel analytique, de la forme “somme de carrés”, avec la condition d’Hörmander réalisée. Soit $q$ un point caractéristique de $P$ . On suppose que $q$ est un point d’un “symplectic Poisson stratum” de codimension deux (au sens de Treves). D’après le théorème d’Okaji, $P$ est hypoelliptique analytique en $q$ . Autrement dit, la conjecture de Treves est vraie en codimension deux. On donne dans ce travail une preuve élémentaire de ce fait.

Let $P$ be a linear partial differential operator with analytic coefficients. We assume that $P$ is of the form “sum of squares”, satisfying Hörmander’s bracket condition. Let $q$ be a characteristic point for $P$ . We assume that $q$ lies on a symplectic Poisson stratum of codimension two. General results of Okaji show that $P$ is analytic hypoelliptic at $q$ . Hence Okaji has established the validity of Treves’ conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Publié le : 2009-01-01

MR 2521430 | Zbl 1178.35138

DOI : https://doi.org/10.5802/aif.2442
Classification: 35H10, 35H20, 35A17, 35A20, 35A27
Mots clés: hypoelliptique analytique, somme de carrés

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     author = {Cordaro, Paulo D. and Hanges, Nicholas},
     title = {A New Proof of Okaji's Theorem  for a Class of Sum of Squares Operators},
     journal = {Annales de l'Institut Fourier},
     volume = {59},
     year = {2009},
     pages = {595-619},
     doi = {10.5802/aif.2442},
     zbl = {1178.35138},
     mrnumber = {2521430},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2009__59_2_595_0}
}

Cordaro, Paulo D.; Hanges, Nicholas. A New Proof of Okaji’s Theorem  for a Class of Sum of Squares Operators. Annales de l'Institut Fourier, Tome 59 (2009) pp. 595-619. doi : 10.5802/aif.2442. http://gdmltest.u-ga.fr/item/AIF_2009__59_2_595_0/

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