On the lowest index for semi-elliptic operators to be Gevrey hypoelliptic (Q1098996)

This paper deals with a class of semi-elliptic differential operators having analytic coefficients. It is well-known that these operators are Gevrey hypoelliptic in each Gevrey class \(\gamma^{(s)}\) if \(s\geq s_ 0=\max (m_ i/m_ j)\) where \(m_ i\in {\mathbb{Z}}\setminus 0\) are fixed integers. The author proves in his main theorem that the same operators are not \(\gamma^{(s)}\) hypoelliptic if \(1\leq s<s_ 0\).