Related papers: On a class of globally analytic Hypoelliptic opera…

The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced in "Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture" by P. Albano and A. Bove and M.…

We consider sums of squares operators globally defined on the torus. We show that if some assumptions are satisfied the operators are globally analytic hypoelliptic. The purpose of the assumptions is to rule out the existence of a Hamilton…

We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the H\"ormander condition and…

We obtain global analytic hypoellipticity for a class of differential operators that can be expressed as a zero-order perturbation of a sum of squares of vector fields with real-analytic coefficients on compact Lie groups. The key…

A global real analytic regularity theorem for a quasilinear sum of squares of vector fields of Hormander rank 2 is given. A related local result for a special case was proved recently by the second author and L. Zanghirati in a paper titled…

This paper provides a complete characterization of global hypoellipticity and solvability with loss of derivatives for Fourier multiplier operators on the $n$-dimensional torus. We establish necessary and sufficient conditions for these…

On $T \times G$, where $T$ is a compact real-analytic manifold and $G$ is a compact Lie group, we consider differential operators $P$ which are invariant by left translations on $G$ and are elliptic in $T$. Under a mild technical condition,…

A simple geometric condition is sufficient for analytic hypoellipticity of sums of squares of two vector fields in ${\mathbb R}^2$. This condition is proved to be necessary for generic vector fields and for various special cases, and to be…

Certain second-order partial differential operators, which are expressed as sums of squares of real-analytic vector fields in $\Bbb R^3$ and which are well known to be $C^\infty$ hypoelliptic, fail to be analytic hypoelliptic.

The recent example of Hanges: $P = \partial_t^2 + t^2\Delta_x + \partial^2_{\theta(x)}$ in $R^3$ is analytic hypoelliptic in the sense of germs but not in the strong sense in any neighborhood of the origin. And its characteristic variety is…

In this work, we present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on a product of compact Riemannian manifolds $T \times G$, where $G$ is also a Lie group. These new…

In this paper, we present necessary and sufficient conditions to have global analytic hypoellipticity for a class of first-order operators defined on $\mathbb{T}^1 \times \mathbb{S}^3$. In the case of real-valued coefficients, we prove that…

This article studies the global hypoellipticity of a class of overdetermined systems of pseudo-differential operators defined on the torus. The main goal consists in establishing connections between the global hypoellipticity of the system…

We are concerned with the problem of real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata…

The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity…

For the hypoelliptic differential operators $P={\partial^2_ x}+(x^k\partial_ y -x^l{\partial_t})^2$ introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of $k$ and $l$ left open in the analysis, the operators $P$ also…

We prove local real analytic hypoellipticity for a sum of squares of complex vector fields studied by J.J. Kohn in a paper to appear in the Annals of Mathematics entitled "Hypoellipticity and loss of derivatives". The operator exhibits a…

Let $L_j = \partial_{t_j} + (a_j+ib_j)(t_j) \partial_x, \, j = 1, \dots, n,$ be a system of vector fields defined on the torus $\mathbb{T}_t^{n}\times\mathbb{T}_x^1$, where the coefficients $a_j$ and $b_j$ are real-valued functions…

In this paper we establish a hypoellipticity result for second order linear operators comprised by a linear combination, with infinite vanishing coefficients, of subelliptic operators in separate spaces. This generalizes previous known…

This note is a comment on a recent paper by J. J. Kohn. We give an example of a second order partial differential operator, expressed as a sum of squares of complex vector fields satisfying the bracket condition, that is not hypoelliptic.