In this paper we consider a class of evolution operators with coefficients depending on time
and space variables (t, x)∈ T× R n, where T is the one-dimensional torus, and prove …

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 …

In this note, we investigate the partial Fourier series on a product of two compact Lie groups.
We give necessary and sufficient conditions for a sequence of partial Fourier coefficients to …

In this paper, we investigate global properties of a class of evolution differential operators
defined on a product of tori and spheres. We present a comprehensive characterization of …

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 note, we investigate Vekua-type periodic operators of the form P u= L u− A u− B u ̄,
where L is a constant coefficient partial differential operator. We provide a complete …

We introduce a class of time-periodic Gelfand-Shilov spaces of functions on T× R n, where
T∼ R/2 π Z is the one-dimensional torus. We develop a Fourier analysis inspired by the …

The main goal of this paper is to address global hypoellipticity issues for the class of first-
order pseudo-differential operators L= D t+ C (t, x, D x), where (t, x)∈ T× M, T is the one …

Analyzing the behavior at infinity of the sequence of eigenvalues given by matrix symbol of a
invariant operator with respect to a fixed elliptic operator, we obtain necessary and sufficient …