Analytic hypoellipticity for operators with symplectic characteristics

A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators

“…The following theorem is our main result, which follows from the work of Okaji [11]. In particular this establishes Treves' conjecture (in the positive direction) in the codimension two case.…”

“…Finally we remark that once the operator P of Theorem 1.2 is written in the special coordinates of section 3, then the regularity result proved in section 4, also follows from the main result of [11]. Our methods are much different from those of [11] and it is our belief that our technique will extend to strata of higher codimension.…”

“…Our methods are much different from those of [11] and it is our belief that our technique will extend to strata of higher codimension. We can also obtain optimal Gevrey regularity results in the codimension two case with our techniques.…”

“…Very general results on analytic hypoellipticity were obtained by Okaji [11] in the symplectic case, allowing non-uniform vanishing of the principal symbol.…”

Gevrey Hypoellipticity for Grushin Operators

“…After then there have been investigated the problem of analytic and non-analytic hypoellipticity of the Grushin operators, (cf. [19], [2], [9], [27], [28], [30], [31], [11]). …”