On certain partial differential operators of finite odd type

Abstract:

Let $P$ be a linear partial differential operator of order $m \geqslant 1$ with real-analytic coefficients defined in $\Omega$, an open set of ${\mathbb {R}^n}$, and let $\gamma$ be in the cotangent space of $\Omega$ minus the zero section. If $P$ is of odd finite type $k$ and if the Hörmander numbers are $1 = {k_1} < {k_2},{k_2}$ odd, then $P$ is analytic hypoelliptic at $\gamma$. These operators are not semirigid.