29 citations · 152 across the 28 of their papers we have counts for
29 papers
Sobolev Regularity in Mixed and Isotropic Scales for Vector Fields on the Torus
Fernando de Ávila Silva, Alexandre Kirilov, André Pedroso Kowacs
We study regularity, existence, and uniqueness of solutions to vector fields on the two-dimensional torus in Sobolev spaces of dominating mixed smoothness, which measure regularity…
Top-Degree Global Solvability for Tube Complexes in Gevrey Ultradistributions
Sandro Coriasco, Alexandre Kirilov, Wagner Augusto Almeida de Moraes +1
Let , let be a connected, non-compact, oriented real-analytic manifold, and let be real-valued closed -forms of Gevrey order on . We study the d…
Vekua-Type Operators on Compact Lie Groups: Hypoellipticity, Solvability, and Self-Duality
Alexandre Kirilov, Ricardo Paleari da Silva
We study global hypoellipticity and global solvability for Vekua-type operators associated with diagonal left-invariant operators on compact Lie groups. The conjugation term produc…
Global Gevrey Hypoellipticity of Involutive Systems on Non-Compact Manifolds
Sandro Coriasco, Alexandre Kirilov, Wagner Augusto Almeida de Moraes +1
We investigate the global Gevrey hypoellipticity of a class of first-order differential operators associated with tube-type involutive structures on , where $M…
Solvability of a class of evolution operators on compact Lie groups
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Pedro Meyer Tokoro
This paper provides sufficient conditions for the solvability of a class of first-order evolution operators of Vekua-type on the product of a one-dimensional torus and a compact Li…
Differential Complexes in Time-Periodic Gelfand-Shilov Spaces
Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov +1
We study the global solvability of a class of differential complexes on the product manifold associated with systems of evolution operators of th…
Global Solvability for Involutive Systems on Non-Compact Manifolds
Sandro Coriasco, Alexandre Kirilov, Wagner Augusto Almeida de Moraes +1
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\time…
Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces
Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov
We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-…
Global hypoellipticity for involutive systems on non-compact manifolds
Sandro Coriasco, Alexandre Kirilov, Wagner Augusto Almeida de Moraes +1
We study the global hypoellipticity of the operator , defined on differential forms over product manifolds of th…
Global Hypoellipticity and Solvability with Loss of Derivatives on the Torus
André Pedroso Kowacs, Alexandre Kirilov
This paper provides a complete characterization of global hypoellipticity and solvability with loss of derivatives for Fourier multiplier operators on the -dimensional torus. We…
Global solutions for systems of strongly invariant operators on closed manifolds
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Pedro Meyer Tokoro
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 Fo…
Diagonal systems of differential operators on compact Lie groups
Paulo L. Dattori da Silva, Alexandre Kirilov, Ricardo Paleari da Silva
We investigate the global hypoellipticity and global solvability of systems of left-invariant differential operators on compact Lie groups. Focusing on diagonal systems, we establi…
Denjoy-Carleman solvability of Vekua-type periodic operators
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Pedro Meyer Tokoro
This paper explores the solvability and global hypoellipticity of Vekua-type differential operators on the n-dimensional torus, within the framework of Denjoy-Carleman ultradiffere…
On the Sobolev boundedness of vector fields on compact Riemannian manifolds
Duván Cardona, Alexandre Kirilov, Wagner A. A. de Moraes +1
We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and mi…
Systems of differential operators in time-periodic Gelfand-Shilov spaces
Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov
This paper explores the global properties of time-independent systems of operators in the framework of Gelfand-Shilov spaces. Our main results provide both necessary and sufficient…
Solvability of Vekua-type periodic operators and applications to classical equations
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Pedro Meyer Tokoro
In this note, we investigate Vekua-type periodic operators of the form , where is a constant coefficient partial differential operator. We provide a complete…
Global solvability and hypoellipticity for evolution operators on tori and spheres
André Pedroso Kowacs, Alexandre Kirilov, Wagner Augusto Almeida de Moraes
In this paper, we study the global properties of a class of evolution-like differential operator with a 0-order perturbation defined on the product of tori and spheres $\…
Global analytic hypoellipticity for a class of evolution operators on
Alexandre Kirilov, Ricardo Paleari da Silva, Wagner Augusto Almeida de Moraes
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…
Global properties of vector fields on compact Lie groups in Komatsu classes. II. Normal forms
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Michael Ruzhansky
Let and be compact Lie groups, , and consider the operator \begin{equation*} L_{aq} = X_1 + a(x_1)X_2 + q(x_1,x_2), \en…
Global and Partial Fourier Series for Denjoy-Carleman Classes on the Torus
Alexandre Kirilov, Bruno de Lessa Victor
In this work, we develop Fourier Analysis for a family of classes of ultradifferentiable functions of Romieu type on the torus, usually known as Denjoy-Carleman classes. Then we ar…
Global properties of vector fields on compact Lie groups in Komatsu classes
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Michael Ruzhansky
In this paper we characterize completely the global hypoellipticity and global solvability in the sense of Komatsu (of Roumieu and Beurling types) of constant-coefficients vector f…
Global hypoellipticity and global solvability for vector fields on compact Lie groups
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Michael Ruzhansky
We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups. In vie…
Partial Fourier series on compact Lie groups
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Michael Ruzhansky
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 coeffic…
Global Hypoellipticity for Strongly Invariant Operators
Alexandre Kirilov, Wagner Augusto Almeida de Moraes
In this note, by analyzing the behavior at infinity of the matrix symbol of an invariant operator with respect to a fixed elliptic operator, we obtain a necessary and sufficien…