Gregorio Chinni

(joint work with Paulo D.~Cordaro)
We study the properties of the Green operator for an analytic linear PDO
such that both it and its formal adjoint are globally sub-elliptic
and globally analytic-hypoelliptic (GAH) in the torus.
We introduce the class of M\'etivier operators, $ \mathscr{M}_{\varepsilon}(\mathbb{T}^{N})$,
study the properties of its perturbations and of its analytic vectors and
show that when the Green operator of $ P(x,D)$
belongs to a well defined class of analytic pseudodifferential operators on the torus
then $ P(x,D) \in \mathscr{M}_{\varepsilon}(\mathbb{T}^{N})$.
We present some examples of linear PDO in such class.\\
We also study (joint work with N. ~Braun Rodrigues, Paulo D.~Cordaro and M.~R.~Jahnke)
the perturbation problem and the Gevrey regularity of the Gevrey vectors
for a class of globally analytic hypoelliptic H\"ormander's operators
defined on the $N$-dimensional torus introduced by P.~D.~ Cordaro and A.~A.Himonas.