非辛Poisson-Treves层上向量场平方和的解析亚椭圆性
Analytic Hypoellipticity at Non-Symplectic Poisson-Treves Strata for Sums of Squares of Vector Fields
摘要：
我们考虑一个算子$ P $，它是具有解析系数的向量场的平方和。该算子具有非辛特征流形，但辛形式$ σ$的秩在$ \Char P $上不是常数。此外，$ P $的Poisson-Treves分层的非辛层的Hamilton叶理由围绕原点的环形开集中的闭曲线组成。证明了$ P $在该开集上是解析亚椭圆的.我们明确地注意到，$ P $的局部Gevrey亚椭圆率是$ G^{k+1} $，并且这是尖锐的。
英文摘要：
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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