Fernando de Ávila Silva

activity

20152026

most citedGlobal hypoellipticity for a class of pseudo-differential operators on the torus

19 citations · 51 across the 7 of their papers we have counts for

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8 papers · 1 filter

math.AP2026

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…

math.AP2026

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 $T^{m} \times R^{n}$ associated with systems of evolution operators of th…

math.AP2024

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…

math.AP2024

Globally solvable time-periodic evolution equations in Gelfand-Shilov classes

Fernando de Ávila Silva, Marco Cappiello

In this paper we consider a class of evolution operators with coefficients depending on time and space variables $(t, x) \in T \times R^{n}$ , where $T$ is t…

math.AP2020

Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators

Fernando de Ávila Silva

This article presents an investigation on the global hypoellipticity problem for systems belonging to the class $P = D_{t} + Q (t, D_{x})$ , where $Q (t, D_{x})$ is a $m \times m$ matrix with…

math.AP2017★ 14 cited

Perturbations of globally hypoelliptic operators on closed manifolds

Fernando de Ávila Silva, Alexandre Kirilov

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…

math.AP2016★ 19 cited

Global hypoellipticity for a class of pseudo-differential operators on the torus

Fernando de Ávila Silva, Rafael Borro Gonzalez, Alexandre Kirilov +1

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

math.AP2015★ 18 cited

Global Hypoellipticity for First-Order Operators on Closed Smooth Manifolds

Fernando de Ávila Silva, Alexandre Kirilov, Todor Gramchev

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 $(t, x) \in T \times M$ , $\mathb…