Fernando Costa Jr.

Universidade Federal da Paraíba - Campus I

Jardim Universitário, s/n, Castelo Branco

CEP 58.051-900, João Pessoa, Brazil

Hi! I’m Fernando Vieira Costa Júnior, a Mathematician from Brazil

Formed with focus on Analysis, I have a particular sympathy for Algebra, Number Theory and Logic. Teaching for me is a passion! In this page I talk a bit about myself and about my job. My students will find here support material for my courses.
(By the way, if you are my student and you’re looking for files, click here).

I am currently associate professor at the Mathematics Department of the Federal Universirty of Paraíba in Brazil. My main research topic is that of Linear Dynamics in Operator Theory (universality, hypercyclicity, recurrence and all that jazz). I am also interested in the classical triad “lineability-spaceability-algebrability”, in some optimization problems and in the implementation of mathematical algorithms in Mathematica and Python.

I also love fractals! (but who doesn’t tbh…)

You can contact me through the email fernando@mat.ufpb.br, although, shall you need a quick response, it is best to write to my personal email fv [dot] costajunior [at] gmail [dot] com.

Selected publications

J. Funct. Anal.

Fernando Costa Jr.

J. Funct. Anal., 2024

Abs Bib

We obtain a multi-dimensional generalization of the Costakis-Sambarino criterion for common hypercyclic vectors with optimal consequences on a large class of fractals. Applications include families of products of backward shifts parameterized by any Hölder continuous curve in \(\mathbb R^d\), for all \(d≥1\).

@article{costa2023self,
  author = {Costa Jr., Fernando},
  title = {<a href="https://doi.org/10.1016/j.jfa.2024.110473">Self-similar fractals and common hypercyclicity</a>},
  journal = {J. Funct. Anal.},
  fjournal = {Journal of Functional Analysis},
  year = {2024},
  pages = {110473},
  issn = {0022-1236},
  mrclass = {47A16(47B37), 28A80, 28A78},
  doi = {10.1016/j.jfa.2024.110473},
  url = {https://doi.org/10.1016/j.jfa.2024.110473},
  keywords = {common hypercyclicity, Hausdorff dimension, self-similar fractal, Hölder curve},
}

Adv. Math.
Baire theorem and hypercyclic algebras

Frédéric Bayart , Fernando Costa Jr., and Dimitris Papathanasiou

Adv. Math., 2021

Abs Bib

The question of whether a hypercyclic operator \(T\) acting on a Fréchet algebra \(X\) admits or not an algebra of hypercyclic vectors (but \(0\)) has been addressed in the recent literature. In this paper we give new criteria and characterisations in the context of convolution operators acting on \(H(\Bbb C)\) and backward shifts acting on a general Fréchet sequence algebra. Analogous questions arise for stronger properties like frequent hypercyclicity. In this trend we give a sufficient condition for a weighted backward shift to admit an upper frequently hypercyclic algebra and we find a weighted backward shift acting on \(c_0\) admitting a frequently hypercyclic algebra for the coordinatewise product. The closed hypercyclic algebra problem is also covered.
@article{MR4178905, author = {Bayart, Fr\'{e}d\'{e}ric and Costa Jr., Fernando and Papathanasiou, Dimitris}, title = {<a href="https://doi.org/10.1016/j.aim.2020.107419">Baire theorem and hypercyclic algebras</a>}, journal = {Adv. Math.}, fjournal = {Advances in Mathematics}, volume = {376}, year = {2021}, pages = {Paper No. 107419, 58}, issn = {0001-8708,1090-2082}, mrclass = {47A16 (46E10 47B48)}, mrnumber = {4178905}, mrreviewer = {Jos\'{e}\ Bonet}, doi = {10.1016/j.aim.2020.107419}, url = {https://doi.org/10.1016/j.aim.2020.107419}, }