This monograph is devoted to the development of the theory of pseudo-di? erential n
operators on spaces with symmetries. Such spaces are the Euclidean space R, the n torus T …

We present conditions on the coefficients of a class of vector fields on the torus which yield a
characterization of global solvability as well as global hypoellipticity, in other words, the …

Let L=∂/∂ t+∑ j= 1 N (a j+ ibj)(t)∂/∂ xj be a vector field defined on the torus T N+ 1≃ R N+
1/2 π Z N+ 1, where aj, bj are real-valued functions and belonging to the Gevrey class G s (T …

We show that an obstruction of number-theoretical nature appears as a necessary condition
for the global hypoellipticity of the pseudo-differential operator L= D_t+ (a+ ib)(t) P (D_x) L …

In this work we consider systems of two smooth vector fields on the three-dimensional torus
associated to a closed 1-form. We prove that, for such systems, the global solvability in the …

The main purpose of this paper is to show, in the two-dimensional torus, a necessary and
sufficient condition in order to certain perturbations of zero order of a system of constant real …

We study the finiteness of range's codimension for a class of non-globally hypoelliptic vector
fields on a torus of dimension three. The linear dependence of certain interactions of the …

The goal of this paper is study the global solvability of a class of complex vector fields of the
special form L=∂/∂ t+ (a+ ib)(x)∂/∂ x, a, b∈ C∞(S1; R), defined on two-torus T2≅ …

We consider a class of systems of two smooth vector fields on the 3-torus associated to a
closed 1-form. We prove that the global solvability is completely determined by the …

This paper deals with Gevrey global solvability on the N-dimensional torus (TN≃ RN/2 π ZN)
to a class of nonlinear first order partial differential equations in the form L u-au-bu¯= f …