Área de interesse 


Tenho me dedicado ao estudo propriedades globais de operadores (pseudo)diferenciais lineares definidos em variedades compactas, ou em todo o espaço euclidiano. Alguns tópicos de investigação são:


Publicações 


2025
  1. de Ávila Silva, F., Coriasco, S., Bonino, M.; Global hypoellipticity for a class of evolution operators in time-periodic weighted Sobolev spaces (2025) (Arxiv)

2024
  1. de Ávila Silva, F., Cappiello, M.,; Globally  solvable time-periodic evolution equations in Gelfand-Shilov classes.  (Mathematische Annalen)
  2. de Ávila Silva, F., Cappiello, M., Kirilov, A.; Systems of differential operators in time-periodic Gelfand-Shilov spaces  (Annali di Matematica Pura ed Applicata)
  3. de Ávila Silva, F.; Medeira, C.;  Globally solvable complexes of pseudo-differential operators on the torus (Arxiv)
  4. de Ávila Silva, F., Cappiello, M., Kirilov, A.; Globally hypoelliptic involutive systems on $T^m x R^n$. (Arxiv)
2023
  1. de Ávila Silva, F.;  Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators (2023) (Math. Nachrichten) (Link)
2022
  1. de Ávila Silva, F.; Cappiello, M.;  Time-periodic Gelfand-Shilov spaces and global hypoellipticity on $\T\times \R^n$ (2022)  (JFA -  Link) 
  2. de Ávila Silva, F.; Machado, E. C.;  Global ultradifferentiable hypoellipticity on compact manifolds (2022) (AdM - Link)
2021
  1. de Ávila Silva, F.; Medeira, C.;  Global  hypoellipticity  for a class of overdetermined systems of pseudo-differential operators on the torus, (2021). (Ann. Mat. Pura Appl. - Link) 
2019
  1. de Ávila Silva, F.; Global hypoellipticity for a class of periodic Cauchy operators. (2019). (J. Math. Anal. Appl. - Link ) 
  2.  de Ávila Silva, F. ;   Kirilov, A.  Perturbations of globally hypoelliptic operators on closed manifolds. (2019)   (Journal of Spectral Theory  - Link)
  3. de Ávila Silva, F. ;  Gonzales, R.; Kirilov, A.; Medeira, C.;  Global hypoellipticity for a class of  pseudo-differential operators on the torus. (2019).    (J. Fourier Anal.  Appl. - Link)    
2018
  1. de Ávila Silva, F. ; Gramchev, T. ; Kirilov, A. . Global Hypoellipticity for First-Order Operators on Closed Smooth Manifolds. (2018). (Journal d'Analyse Mathématique (Jerusalem)  - Link ).   
                                   

Preprint

  1. de Ávila Silva, F., Cappiello, M.,;  Time periodic Gelfand-Shilov classes in the Anisotropic setting.
  2. de Ávila Silva, F.; Machado, E. C.; Global ultradifferentiable  solvability on compact manifolds.
  3. de Ávila Silva, F.; de Morares, W.A.A,  Global properties for a class of periodic-evolution operators on compact manifolds.

Principais apresentações de trabalho


  1. ICMC Summer Meeting on Differential Equations 2025 Chapter. Globally solvable complexes of pseudo-differential operators on the torus. 2025.
  2. II Simpósio de Equações Diferenciais Parciais Lineares e Análise de Fourier Global properties for certain classes of linear equations on T^m x R^n. 2025.
  3. Fourier Analysis and Partial Differential Equations II, 2024, A class of globally hypoelliptic systems of periodic pseudodifferential operators.
  4. 14th International ISAAC Congress, 2023. Global hypoellipticity for a class of systems of periodic P.D.O's.
  5. ICMC Summer Meeting on Differential Equations, 2023. Global ultradifferentiable properties for certain linear operators on compact manifolds. 
  6. 33 Colóquio Brasileiro de Matemática. IMPA, 2021; Time-periodic Gelfand-Shilov spaces and global hypoellipticity for a class of evolution equations.
  7. International Workshop on Operator Theory and its Applications.  Chapman University (US), 2021; Globally hypoelliptic time-periodic evolution equations.
  8. Microlocal and Global Analysis, Interactions with Geometry, Universiy of Potsdam, Alemanha, 2021; Globally hypoelliptic systems of pseudo-differential operators on the torus.
  9. Web Seminar on Linear PDE's and Related Topics (UFPR/USP), 2020; Global hypoellipticity for a class of systems of pseudo-differential operators on the torus.
  10. Seminari di Analisi Matematica, Torino, Itália, 2020; Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators
  11. 10th Workshop on Geometric Analysis of PDEs and Several Complex Variables, Serra Negra, Brasil, 2019; Perturbations of globally hypoelliptic operators on closed manifolds.
  12. Microlocal and Global Analysis, Interactions with Geometry, Inst.  Universiy of Potsdam, Alemanha, 2019; A class of globally hypoelliptic Cauchy operators on the torus and generalized Siegel conditions.
  13. ICMC Summer Meeting on Differential Equations, USP, 2019; A class of globally hypoelliptic Cauchy operators on the torus and generalized Siegel conditions.
  14. III Congresso Brasileiro de Jovens Pesquisadores em Matemática Pura, Aplicada e Estatística, UFPR, 2018; A class of globally hypoelliptic operators on manifolds.
  15. Conference BRICS on Mathematics, Foz do Iguaçu,  2018; Global Hypoellipticity on Manifolds and Fourier Expansion of Elliptic Operators.
  16. International Workshop on Partial Differential Equations and Complex Analysis, UFScar, 2018; Globally hypoelliptic operators on closed manifolds and perturbations.
  17. 9th Workshop on Geometric Analysis of PDEs and Several Complex Variables, Serra Negra, Brasil, 2017; Perturbations of globally hypoelliptic operators on closed manifolds.
  18. A Life in Mathematics Generalized functions, Microlocal analysis, PDEs and Dynamical systems Conference in memory of Todor V. Gramchev. Torino, Itália, 2017; Perturbations od Globally Hypoelliptic Invariant Operators on Smooth Manifolds.