Related papers: Global hypoellipticity for involutive systems on n…
We investigate the global Gevrey hypoellipticity of a class of first-order differential operators associated with tube-type involutive structures on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold diffeomorphic to the interior of…
We establish necessary and sufficient conditions for the closedness of the range of a class of first-order differential operators associated with an involutive structure on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold…
We study the global hypoellipticity and solvability of strongly invariant operators and systems of strongly invariant operators on closed manifolds. Our approach is based on the Fourier analysis induced by an elliptic pseudo-differential…
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…
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…
We apply the characterization of global hypoellipticity for $G$-invariant operators on homogeneous vector bundles obtained by Cardona and Kowacs [J. Pseudo-Differ. Oper. Appl. 16, 23 (2025)] to obtain a necessary and sufficient condition…
We study in this paper the global hypoellipticity property in the Gevrey category for the generalized twisted Laplacian on forms. Different from the 0-form case, where the twisted Laplacian is a scalar operator, this is a system of…
We study the global hypoellipticity problem for certain linear operators in Komatsu classes of Roumieu and Beurling type on compact manifolds. We present an approach by combining a characterization of these spaces via eigenfuction…
The main goal of this paper is to address global hypoellipticity issues for the following class of operators: $L = D_t + C(t,x,D_x)$, where $(t,x) \in \mathbb{T} \times M$, $\mathbb{T}$ is the one-dimensional torus, $M$ is a closed manifold…
Inspired by results of A. Bergamasco on perturbations of vector fields defined on the two-dimensional torus, and of J. Delgado and M. Ruzhansky on properties of invariant operators with respect to an elliptic operator defined on a closed…
We investigate the global hypoellipticity and global solvability of systems of left-invariant differential operators on compact Lie groups. Focusing on diagonal systems, we establish necessary and sufficient conditions for these global…
We introduce time-periodic Gevrey-Sobolev-Kato spaces on asymptotically Euclidean manifolds and study their characterisation throughout Fourier expansions associated with suitable elliptic operators. As an application, we study the global…
In this paper, we study Vekua-type operators associated with diagonal operators on compact Lie groups. Characterizations of global hypoellipticity and global solvability properties are presented on classes of Vekua-type operators with…
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,…
Given a contact sub-Riemannian manifold one obtains a non-integrable splitting of the tangent bundle into the directions along the contact distribution and the Reeb field. We generalize the construction of the Bismut superconnection to this…
This note presents an investigation on the global hypoellipticity problem for Cauchy operators on $\mathbb{T}^{n+1}$ belonging to the class \linebreak $L = \prod_{j=1}^{m}\left(D_t + c_j(t) P_j(D_x)\right)$, where $P_j(D_x)$ is a…
In this note, by analyzing the behavior at infinity of the matrix symbol of an invariant operator $P$ with respect to a fixed elliptic operator, we obtain a necessary and sufficient condition to guarantee that $P$ is globally hypoelliptic.…
Examples are given of degenerate elliptic operators on smooth, compact manifolds that are not globally regular in $C^\infty$. These operators degenerate only in a rather mild fashion. Certain weak regularity results are proved, and an…
In this article we reconsider the proof of subelliptic estimates for Geometric Kramers-Fokker-Planck operators, a class which includes Bismut's hypoelliptic Laplacian, when the base manifold is closed (no boundary). The method is…
Let $\mathcal{M}$ be a compact, smooth, $n$-dimensional Riemannian manifold without boundary. In this paper, we generalize nonwindowed geometric scattering transforms, which we formulate as $\mathbf{L}^q(\mathcal{M})$ norms of a cascade of…