Analytic Hypoellipticity at Non-Symplectic Poisson-Treves Strata for Sums of Squares of Vector Fields

2006/09/28 by Antonio Bove, Bove, Antonio, David S. Tartakoff +1
Computer Science · Mathematics · #35H10 #35N15 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35H10 #msc:35N15

paper · pdf · doi:10.48550/arxiv.math/0609777

20pp

arxiv created 2006/09/28 · openalex publication_date 2006/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an operator P which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form σ is not constant on \Char P . Moreover the Hamilton foliation of the non symplectic stratum of the Poisson-Treves stratification for P consists of closed curves in a ring-shaped open set around the origin. We prove that then P is analytic hypoelliptic on that open set. And we note explicitly that the local Gevrey hypoellipticity for P is G^k+1 and that this is sharp.

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