Let be a linear partial differential operator with analytic coefficients. We assume that is of the form “sum of squares”, satisfying Hörmander’s bracket condition. Let be a characteristic point for . We assume that lies on a symplectic Poisson stratum of codimension two. General results of Okaji show that is analytic hypoelliptic at . 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.
Soit un opérateur différentiel analytique, de la forme “somme de carrés”, avec la condition d’Hörmander réalisée. Soit un point caractéristique de . On suppose que est un point d’un “symplectic Poisson stratum” de codimension deux (au sens de Treves). D’après le théorème d’Okaji, est hypoelliptique analytique en . Autrement dit, la conjecture de Treves est vraie en codimension deux. On donne dans ce travail une preuve élémentaire de ce fait.
Keywords: Analytic hypoelliptic, sum of squares
Mot clés : hypoelliptique analytique, somme de carrés
@article{AIF_2009__59_2_595_0, author = {Cordaro, Paulo D. and Hanges, Nicholas}, title = {A {New} {Proof} of {Okaji{\textquoteright}s} {Theorem} for a {Class} of {Sum} of {Squares} {Operators}}, journal = {Annales de l'Institut Fourier}, pages = {595--619}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {59}, number = {2}, year = {2009}, doi = {10.5802/aif.2442}, zbl = {1178.35138}, mrnumber = {2521430}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2442/} }
TY - JOUR AU - Cordaro, Paulo D. AU - Hanges, Nicholas TI - A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators JO - Annales de l'Institut Fourier PY - 2009 SP - 595 EP - 619 VL - 59 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2442/ DO - 10.5802/aif.2442 LA - en ID - AIF_2009__59_2_595_0 ER -
%0 Journal Article %A Cordaro, Paulo D. %A Hanges, Nicholas %T A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators %J Annales de l'Institut Fourier %D 2009 %P 595-619 %V 59 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2442/ %R 10.5802/aif.2442 %G en %F 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, Volume 59 (2009) no. 2, pp. 595-619. doi : 10.5802/aif.2442. http://archive.numdam.org/articles/10.5802/aif.2442/
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