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

Paulo D. Cordaro^{[1]}; Nicholas Hanges^{[2]}

- [1] Universidade de São Paulo São Paulo, SP (Brazil)
- [2] Lehman College Department of Mathematics/CUNY Bronx, New York 10468 (USA)

Annales de l’institut Fourier (2009)

- Volume: 59, Issue: 2, page 595-619
- ISSN: 0373-0956

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topCordaro, Paulo D., and Hanges, Nicholas. "A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators." Annales de l’institut Fourier 59.2 (2009): 595-619. <http://eudml.org/doc/10406>.

@article{Cordaro2009,

abstract = {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.},

affiliation = {Universidade de São Paulo São Paulo, SP (Brazil); Lehman College Department of Mathematics/CUNY Bronx, New York 10468 (USA)},

author = {Cordaro, Paulo D., Hanges, Nicholas},

journal = {Annales de l’institut Fourier},

keywords = {Analytic hypoelliptic; sum of squares; analytic hypoelliptic; symplectic Poisson strata},

language = {eng},

number = {2},

pages = {595-619},

publisher = {Association des Annales de l’institut Fourier},

title = {A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators},

url = {http://eudml.org/doc/10406},

volume = {59},

year = {2009},

}

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

PB - Association des Annales de l’institut Fourier

VL - 59

IS - 2

SP - 595

EP - 619

AB - 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.

LA - eng

KW - Analytic hypoelliptic; sum of squares; analytic hypoelliptic; symplectic Poisson strata

UR - http://eudml.org/doc/10406

ER -

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